Training machine learning potentials for reactive systems: A Colab tutorial on basic models.

In the last several years, there has been a surge in the development of machine learning potential (MLP) models for describing molecular systems. We are interested in a particular area of this field - the training of system-specific MLPs for reactive systems - with the goal of using these MLPs to accelerate free energy simulations of chemical and enzyme reactions. To help new members in our labs become familiar with the basic techniques, we have put together a self-guided Colab tutorial (https://cc-ats.github.io/mlp_tutorial/), which we expect to be also useful to other young researchers in the community. Our tutorial begins with the introduction of simple feedforward neural network (FNN) and kernel-based (using Gaussian process regression, GPR) models by fitting the two-dimensional Müller-Brown potential. Subsequently, two simple descriptors are presented for extracting features of molecular systems: symmetry functions (including the ANI variant) and embedding neural networks (such as DeepPot-SE). Lastly, these features will be fed into FNN and GPR models to reproduce the energies and forces for the molecular configurations in a Claisen rearrangement reaction.

Bridging semiempirical and ab initio QM/MM potentials by Gaussian process regression and its sparse variants for free energy simulation.

Free energy simulations that employ combined quantum mechanical and molecular mechanical (QM/MM) potentials at ab initio QM (AI) levels are computationally highly demanding. Here, we present a machine-learning-facilitated approach for obtaining AI/MM-quality free energy profiles at the cost of efficient semiempirical QM/MM (SE/MM) methods. Specifically, we use Gaussian process regression (GPR) to learn the potential energy corrections needed for an SE/MM level to match an AI/MM target along the minimum free energy path (MFEP). Force modification using gradients of the GPR potential allows us to improve configurational sampling and update the MFEP. To adaptively train our model, we further employ the sparse variational GP (SVGP) and streaming sparse GPR (SSGPR) methods, which efficiently incorporate previous sample information without significantly increasing the training data size. We applied the QM-(SS)GPR/MM method to the solution-phase SN2 Menshutkin reaction, NH3+CH3Cl→CH3NH3++Cl-, using AM1/MM and B3LYP/6-31+G(d,p)/MM as the base and target levels, respectively. For 4000 configurations sampled along the MFEP, the iteratively optimized AM1-SSGPR-4/MM model reduces the energy error in AM1/MM from 18.2 to 4.4 kcal/mol. Although not explicitly fitting forces, our method also reduces the key internal force errors from 25.5 to 11.1 kcal/mol/Å and from 30.2 to 10.3 kcal/mol/Å for the N-C and C-Cl bonds, respectively. Compared to the uncorrected simulations, the AM1-SSGPR-4/MM method lowers the predicted free energy barrier from 28.7 to 11.7 kcal/mol and decreases the reaction free energy from -12.4 to -41.9 kcal/mol, bringing these results into closer agreement with their AI/MM and experimental benchmarks.

Facilitating ab initio QM/MM free energy simulations by Gaussian process regression with derivative observations.

In combined quantum mechanical and molecular mechanical (QM/MM) free energy simulations, how to synthesize the accuracy of ab initio (AI) methods with the speed of semiempirical (SE) methods for a cost-effective QM treatment remains a long-standing challenge. In this work, we present a machine-learning-facilitated method for obtaining AI/MM-quality free energy profiles through efficient SE/MM simulations. In particular, we use Gaussian process regression (GPR) to learn the energy and force corrections needed for SE/MM to match with AI/MM results during molecular dynamics simulations. Force matching is enabled in our model by including energy derivatives into the observational targets through the extended-kernel formalism. We demonstrate the effectiveness of this method on the solution-phase SN2 Menshutkin reaction using AM1/MM and B3LYP/6-31+G(d,p)/MM as the base and target levels, respectively. Trained on only 80 configurations sampled along the minimum free energy path (MFEP), the resulting GPR model reduces the average energy error in AM1/MM from 18.2 to 5.8 kcal mol-1 for the 4000-sample testing set with the average force error on the QM atoms decreased from 14.6 to 3.7 kcal mol-1 Å-1. Free energy sampling with the GPR corrections applied (AM1-GPR/MM) produces a free energy barrier of 14.4 kcal mol-1 and a reaction free energy of -34.1 kcal mol-1, in closer agreement with the AI/MM benchmarks and experimental results.

Accelerated computation of free energy profile at ab initio quantum mechanical/molecular mechanical accuracy via a semi-empirical reference potential. II. Recalibrating semi-empirical parameters with force matching.

An efficient and accurate reference potential simulation protocol is proposed for producing ab initio quantum mechanical/molecular mechanical (AI-QM/MM) quality free energy profiles for chemical reactions in a solvent or macromolecular environment. This protocol involves three stages: (a) using force matching to recalibrate a semi-empirical quantum mechanical (SE-QM) Hamiltonian for the specific reaction under study; (b) employing the recalibrated SE-QM Hamiltonian (in combination with molecular mechanical force fields) as the reference potential to drive umbrella samplings along the reaction pathway; and (c) computing AI-QM/MM energy values for collected configurations from the sampling and performing weighted thermodynamic perturbation to acquire an AI-QM/MM corrected reaction free energy profile. For three model reactions (identity SN2 reaction, Menshutkin reaction, and glycine proton transfer reaction) in aqueous solution and one enzyme reaction (Claisen arrangement in chorismate mutase), our simulations using recalibrated PM3 SE-QM Hamiltonians well reproduced QM/MM free energy profiles at the B3LYP/6-31G* level of theory all within 1 kcal mol-1 with a 20 to 45 fold reduction in the computer time.

Exploring Cycloreversion Reaction of Cyclobutane Pyrimidine Dimers Quantum Mechanically.

The cyclobutane pyrimidine dimer (CPD) is a major photoproduct of deoxyribonucleic acid (DNA) that is damaged by ultraviolet light. This DNA lesion can be repaired by DNA photolyase with the aid of UV light and two cofactors. To understand the repair mechanism of CPD and whether protonation of CPD participates in the DNA repair process, the cycloreversion reactions of four CPD models and proton transfers between the adjacent residue Glu283 and CPD models were explored through the quantum mechanical method. Two-dimensional maps of potential energy surface in a vacuum and in implicit water solution were calculated at the ωB97XD/6-311++G(2df,2pd) level. One-dimensional potential energy profiles were computed for proton transfer reactions. Among the models that have been considered, both in a vacuum and in water solution, the results indicate that the most likely repair mechanism involves CPD•2- radical anion splitting in a stepwise manner. C5-C5' splits first, and C6-C6' splits later. The computed free energies of activation of the two splitting steps are 0.9 and 3.1 kcal/mol, respectively. The adjacent Glu283 may stabilize the CPD•2- radical anion through hydrogen bond and increase the quantum yield; however, protonating the CPD radical anion by Glu283 cannot accelerate the rate of ring opening.

Mapping Free Energy Pathways for ATP Hydrolysis in the E. coli ABC Transporter HlyB by the String Method.

HlyB functions as an adenosine triphosphate (ATP)-binding cassette (ABC) transporter that enables bacteria to secrete toxins at the expense of ATP hydrolysis. Our previous work, based on potential energy profiles from combined quantum mechanical and molecular mechanical (QM/MM) calculations, has suggested that the highly conserved H-loop His residue H662 in the nucleotide binding domain (NBD) of E. coli HlyB may catalyze the hydrolysis of ATP through proton relay. To further test this hypothesis when entropic contributions are taken into account, we obtained QM/MM minimum free energy paths (MFEPs) for the HlyB reaction, making use of the string method in collective variables. The free energy profiles along the MFEPs confirm the direct participation of H662 in catalysis. The MFEP simulations of HlyB also reveal an intimate coupling between the chemical steps and a local protein conformational change involving the signature-loop residue S607, which may serve a catalytic role similar to an Arg-finger motif in many ATPases and GTPases in stabilizing the phosphoryl-transfer transition state.

Trapping the ATP binding state leads to a detailed understanding of the F1-ATPase mechanism.

The rotary motor enzyme FoF1-ATP synthase uses the proton-motive force across a membrane to synthesize ATP from ADP and Pi (H2PO4(-)) under cellular conditions that favor the hydrolysis reaction by a factor of 2 × 10(5). This remarkable ability to drive a reaction away from equilibrium by harnessing an external force differentiates it from an ordinary enzyme, which increases the rate of reaction without shifting the equilibrium. Hydrolysis takes place in the neighborhood of one conformation of the catalytic moiety F1-ATPase, whose structure is known from crystallography. By use of molecular dynamics simulations we trap a second structure, which is rotated by 40° from the catalytic dwell conformation and represents the state associated with ATP binding, in accord with single-molecule experiments. Using the two structures, we show why Pi is not released immediately after ATP hydrolysis, but only after a subsequent 120° rotation, in agreement with experiment. A concerted conformational change of the α3ß3 crown is shown to induce the 40° rotation of the γ-subunit only when the ßE subunit is empty, whereas with Pi bound, ßE serves as a latch to prevent the rotation of γ. The present results provide a rationalization of how F1-ATPase achieves the coupling between the small changes in the active site of ßDP and the 40° rotation of γ.

Treating electrostatics with Wolf summation in combined quantum mechanical and molecular mechanical simulations.

The Wolf summation approach [D. Wolf et al., J. Chem. Phys. 110, 8254 (1999)], in the damped shifted force (DSF) formalism [C. J. Fennell and J. D. Gezelter, J. Chem. Phys. 124, 234104 (2006)], is extended for treating electrostatics in combined quantum mechanical and molecular mechanical (QM/MM) molecular dynamics simulations. In this development, we split the QM/MM electrostatic potential energy function into the conventional Coulomb r(-1) term and a term that contains the DSF contribution. The former is handled by the standard machinery of cutoff-based QM/MM simulations whereas the latter is incorporated into the QM/MM interaction Hamiltonian as a Fock matrix correction. We tested the resulting QM/MM-DSF method for two solution-phase reactions, i.e., the association of ammonium and chloride ions and a symmetric SN2 reaction in which a methyl group is exchanged between two chloride ions. The performance of the QM/MM-DSF method was assessed by comparing the potential of mean force (PMF) profiles with those from the QM/MM-Ewald and QM/MM-isotropic periodic sum (IPS) methods, both of which include long-range electrostatics explicitly. For ion association, the QM/MM-DSF method successfully eliminates the artificial free energy drift observed in the QM/MM-Cutoff simulations, in a remarkable agreement with the two long-range-containing methods. For the SN2 reaction, the free energy of activation obtained by the QM/MM-DSF method agrees well with both the QM/MM-Ewald and QM/MM-IPS results. The latter, however, requires a greater cutoff distance than QM/MM-DSF for a proper convergence of the PMF. Avoiding time-consuming lattice summation, the QM/MM-DSF method yields a 55% reduction in computational cost compared with the QM/MM-Ewald method. These results suggest that, in addition to QM/MM-IPS, the QM/MM-DSF method may serve as another efficient and accurate alternative to QM/MM-Ewald for treating electrostatics in condensed-phase simulations of chemical reactions.

Assessing the accuracy of the isotropic periodic sum method through Madelung energy computation.

We tested the isotropic periodic sum (IPS) method for computing Madelung energies of ionic crystals. The performance of the method, both in its nonpolar (IPSn) and polar (IPSp) forms, was compared with that of the zero-charge and Wolf potentials [D. Wolf, P. Keblinski, S. R. Phillpot, and J. Eggebrecht, J. Chem. Phys. 110, 8254 (1999)]. The results show that the IPSn and IPSp methods converge the Madelung energy to its reference value with an average deviation of ∼10(-4) and ∼10(-7) energy units, respectively, for a cutoff range of 18-24a (a/2 being the nearest-neighbor ion separation). However, minor oscillations were detected for the IPS methods when deviations of the computed Madelung energies were plotted on a logarithmic scale as a function of the cutoff distance. To remove such oscillations, we introduced a modified IPSn potential in which both the local-region and long-range electrostatic terms are damped, in analogy to the Wolf potential. With the damped-IPSn potential, a smoother convergence was achieved. In addition, we observed a better agreement between the damped-IPSn and IPSp methods, which suggests that damping the IPSn potential is in effect similar to adding a screening potential in IPSp.

H-loop histidine catalyzes ATP hydrolysis in the E. coli ABC-transporter HlyB.

Adenosine triphosphate (ATP)-binding cassette (ABC) transporters form a family of molecular motor proteins that couple ATP hydrolysis to substrate translocation across cell membranes. Each nucleotide binding domain of ABC-transporters contains a highly conserved H-loop histidine residue, whose precise mechanistic role in motor functions has remained elusive. By using combined quantum mechanical and molecular mechanical (QM/MM) calculations, we showed that the conserved H-loop residue H662 in E. coli HlyB, a bacterial ABC-transporter, can act first as a general acid and then as a general base to facilitate proton transfer in ATP hydrolysis. Without the assistance of H662, direct proton transfer from the lytic water to ATP results in a substantially higher barrier height. Our findings suggest that the essential function of the H-loop residue H662 is to provide a "chemical linchpin" that shuttles protons between reactants through a relay mechanism, thereby catalyzing ATP hydrolysis in HlyB.

Revealing intrinsic changes of DNA induced by spore photoproduct lesion through computer simulation.

In bacterial endospores, a cross-linked thymine dimer, 5-thyminyl-5,6-dihydrothymine, commonly referred to as the spore photoproduct (SP), is found as the dominant DNA photo lesion under UV radiation. During spore germination, SP is faithfully repaired by the spore photoproduct lyase (SPL) for normal DNA replication to resume. Despite this general mechanism, the exact way in which SP modifies the duplex DNA structure so that the damaged site can be recognized by SPL to initiate the repair process is still unclear. A previous X-ray crystallographic study, which used a reverse transcriptase as a DNA host template, captured a protein-bound duplex oligonucleotide containing two SP lesions; the study showed shortened hydrogen bonds between the AT base pairs involved in the lesions and widened minor grooves near the damaged sites. However, it remains to be determined whether the results accurately reflect the conformation of SP-containing DNA (SP-DNA) in its fully hydrated pre-repair form. To uncover the intrinsic changes in DNA conformation caused by SP lesions, we performed molecular dynamics (MD) simulations of SP-DNA duplexes in aqueous solution, using the nucleic acid portion of the previously determined crystal structure as a template. After MD relaxation, our simulated SP-DNAs showed weakened hydrogen bonds at the damaged sites compared to those in the undamaged DNA. Our analyses of the MD trajectories revealed a range of local and global structural distortions of DNA induced by SP. Specifically, the SP region displays a greater tendency to adopt an A-like-DNA conformation, and curvature analysis revealed an increase in the global bending compared to the canonical B-DNA. Although these SP-induced DNA conformational changes are relatively minor, they may provide a sufficient structural basis for SP to be recognized by SPL during the lesion repair process.

Free Energy Profile Decomposition Analysis for QM/MM Simulations of Enzymatic Reactions.

In enzyme mechanistic studies and mutant design, it is highly desirable to know the individual residue contributions to the reaction free energy and barrier. In this work, we show that such free energy contributions from each residue can be readily obtained by postprocessing ab initio quantum mechanical molecular mechanical (ai-QM/MM) free energy simulation trajectories. Specifically, through a mean force integration along the minimum free energy pathway, one can obtain the electrostatic, polarization, and van der Waals contributions from each residue to the free energy barrier. Separately, a similar analysis procedure allows us to assess the contribution from different collective variables along the reaction coordinate. The chorismate mutase reaction is used to demonstrate the utilization of these two trajectory analysis tools.

Hybrid Metal-Ligand Interfacial Dipole Engineering of Functional Plasmonic Nanostructures for Extraordinary Responses of Optoelectronic Properties.

Programmable manipulation of inorganic-organic interfacial electronic properties of ligand-functionalized plasmonic nanoparticles (NPs) is the key parameter dictating their applications such as catalysis, photovoltaics, and biosensing. Here we report the localized surface plasmon resonance (LSPR) properties of gold triangular nanoprisms (Au TNPs) in solid state that are functionalized with dipolar, conjugated ligands. A library of thiocinnamate ligands with varying surface dipole moments were used to functionalize TNPs, which results in ∼150 nm reversible tunability of LSPR peak wavelength with significant peak broadening (∼230 meV). The highly adjustable chemical system of thiocinnamate ligands is capable of shifting the Au work function down to 2.4 eV versus vacuum, i.e., ∼2.9 eV lower than a clean Au (111) surface, and this work function can be modulated up to 3.3 eV, the largest value reported to date through the formation of organothiolate SAMs on Au. Interestingly, the magnitude of plasmonic responses and work function modulation is NP shape dependent. By combining first-principles calculations and experiments, we have established the mechanism of direct wave function delocalization of electrons residing near the Fermi level into hybrid electronic states that are mostly dictated by the inorganic-organic interfacial dipole moments. We determine that both interfacial dipole and hybrid electronic states, and vinyl conjugation together are the key to achieving such extraordinary changes in the optoelectronic properties of ligand-functionalized, plasmonic NPs. The present study provides a quantitative relationship describing how specifically constructed organic ligands can be used to control the interfacial properties of NPs and thus the plasmonic and electronic responses of these functional plasmonics for a wide range of plasmon-driven applications.

Machine learning based implicit solvent model for aqueous-solution alanine dipeptide molecular dynamics simulations.

Inspired by the recent work from Noé and coworkers on the development of machine learning based implicit solvent model for the simulation of solvated peptides [Chen et al., J. Chem. Phys., 2021, 155, 084101], here we report another investigation of the possibility of using machine learning (ML) techniques to "derive" an implicit solvent model directly from explicit solvent molecular dynamics (MD) simulations. For alanine dipeptide, a machine learning potential (MLP) based on the DeepPot-SE representation of the molecule was trained to capture its interactions with its average solvent environment configuration (ASEC). The predicted forces on the solute deviated only by an RMSD of 0.4 kcal mol-1 Å-1 from the reference values, and the MLP-based free energy surface differed from that obtained from explicit solvent MD simulations by an RMSD of less than 0.9 kcal mol-1. Our MLP training protocol could also accurately reproduce combined quantum mechanical molecular mechanical (QM/MM) forces on the quantum mechanical (QM) solute in ASEC environment, thus enabling the development of accurate ML-based implicit solvent models for ab initio-QM MD simulations. Such ML-based implicit solvent models for QM calculations are cost-effective in both the training stage, where the use of ASEC reduces the number of data points to be labelled, and the inference stage, where the MLP can be evaluated at a relatively small additional cost on top of the QM calculation of the solute.

Expanding the horizon of the thymine isostere biochemistry: unique cyclobutane dimers formed by photoreaction between a thymine and a toluene residue in the dinucleotide framework.

Substituted toluenyl groups are considered as close isosteres of the thymine residue. They can be recognized by DNA polymerases as if they were thymine. These toluene derivatives are generally inert toward radical additions, including the [2+2] photo-cycloadditions, due to the stable structure of the aromatic ring and are usually used as solvents for radical reactions. Surprisingly, after incorporating toluene into the dinucleotide framework, we found that the UV excited thymine residue readily dimerizes with the toluenyl moiety through a [2+2] photo-addition reaction. Furthermore, the reaction site on the toluenyl moiety is not the C5=C6 bond, as commonly observed in cyclobutane pyrimidine dimers, but the C4=C5 or C3=C4 instead. Such a reaction pattern suggests that in the stacked structure, it is one of these bonds, not the C5=C6, that is close to the thymine C5=C6 bond. A similar structural feature is found in DNA duplex with a thymine replaced by a 2,4-difluorotoluene. Our results argue that although the substituted toluenyl moieties closely mimic the size and shape of the thymine residue, their more hydrophobic nature determines that they stack on DNA bases differently from the natural thymine residue and likely cause local conformational changes in duplex DNA.

Accelerating Ab Initio Quantum Mechanical and Molecular Mechanical (QM/MM) Molecular Dynamics Simulations with Multiple Time Step Integration and a Recalibrated Semiempirical QM/MM Hamiltonian.

Molecular dynamics (MD) simulations employing ab initio quantum mechanical and molecular mechanical (ai-QM/MM) potentials are considered to be the state of the art, but the high computational cost associated with the ai-QM calculations remains a theoretical challenge for their routine application. Here, we present a modified protocol of the multiple time step (MTS) method for accelerating ai-QM/MM MD simulations of condensed-phase reactions. Within a previous MTS protocol [Nam J. Chem. Theory Comput. 2014, 10, 4175], reference forces are evaluated using a low-level (semiempirical QM/MM) Hamiltonian and employed at inner time steps to propagate the nuclear motions. Correction forces, which arise from the force differences between high-level (ai-QM/MM) and low-level Hamiltonians, are applied at outer time steps, where the MTS algorithm allows the time-reversible integration of the correction forces. To increase the outer step size, which is bound by the highest-frequency component in the correction forces, the semiempirical QM Hamiltonian is recalibrated in this work to minimize the magnitude of the correction forces. The remaining high-frequency modes, which are mainly bond stretches involving hydrogen atoms, are then removed from the correction forces. When combined with a Langevin or SIN(R) thermostat, the modified MTS-QM/MM scheme remains robust with an up to 8 (with Langevin) or 10 fs (with SIN(R)) outer time step (with 1 fs inner time steps) for the chorismate mutase system. This leads to an over 5-fold speedup over standard ai-QM/MM simulations, without sacrificing the accuracy in the predicted free energy profile of the reaction.

Chemical synthesis, crystal structure and enzymatic evaluation of a dinucleotide spore photoproduct analogue containing a formacetal linker.

Spore photoproduct (SP) is the exclusive DNA photodamage product found in bacterial endospores. Its photoformation and repair by a metalloenzyme spore photoproduct lyase (SPL) composes the unique SP biochemistry. Despite the fact that the SP was discovered almost 50 years ago, its crystal structure is still unknown and the lack of structural information greatly hinders the study of SP biochemistry. Employing a formacetal linker and organic synthesis, we successfully prepared a dinucleotide SP isostere 5R-CH(2) SP, which contains a neutral CH(2) moiety between the two thymine residues instead of a phosphate. The neutral linker dramatically facilitates the crystallization process, allowing us to obtain the crystal structure for this intriguing thymine dimer half a century after its discovery. Further ROESY spectroscopic, DFT computational, and enzymatic studies of this 5R-CH(2) SP compound prove that it possesses similar properties with the 5R-SP species, suggesting that the revealed structure truly reflects that of SP generated in Nature.

How subunit coupling produces the gamma-subunit rotary motion in F1-ATPase.

F(o)F(1)-ATP synthase manufactures the energy "currency," ATP, of living cells. The soluble F(1) portion, called F(1)-ATPase, can act as a rotary motor, with ATP binding, hydrolysis, and product release, inducing a torque on the gamma-subunit. A coarse-grained plastic network model is used to show at a residue level of detail how the conformational changes of the catalytic beta-subunits act on the gamma-subunit through repulsive van der Waals interactions to generate a torque that drives unidirectional rotation, as observed experimentally. The simulations suggest that the calculated 85 degrees substep rotation is driven primarily by ATP binding and that the subsequent 35 degrees substep rotation is produced by product release from one beta-subunit and a concomitant binding pocket expansion of another beta-subunit. The results of the simulation agree with single-molecule experiments [see, for example, Adachi K, et al. (2007) Cell 130:309-321] and support a tri-site rotary mechanism for F(1)-ATPase under physiological condition.

Doubly Polarized QM/MM with Machine Learning Chaperone Polarizability.

A major shortcoming of semiempirical (SE) molecular orbital methods is their severe underestimation of molecular polarizability compared with experimental and ab initio (AI) benchmark data. In a combined quantum mechanical and molecular mechanical (QM/MM) treatment of solution-phase reactions, solute described by SE methods therefore tends to generate inadequate electronic polarization response to solvent electric fields, which often leads to large errors in free energy profiles. To address this problem, here we present a hybrid framework that improves the response property of SE/MM methods through high-level molecular-polarizability fitting. Specifically, we place on QM atoms a set of corrective polarizabilities (referred to as chaperone polarizabilities), whose magnitudes are determined from machine learning (ML) to reproduce the condensed-phase AI molecular polarizability along the minimum free energy path. These chaperone polarizabilities are then used in a machinery similar to a polarizable force field calculation to compensate for the missing polarization energy in the conventional SE/MM simulations. Because QM atoms in this treatment host SE wave functions as well as classical polarizabilities, both polarized by MM electric fields, we name this method doubly polarized QM/MM (dp-QM/MM). We demonstrate the new method on the free energy simulations of the Menshutkin reaction in water. Using AM1/MM as a base method, we show that ML chaperones greatly reduce the error in the solute molecular polarizability from 6.78 to 0.03 Å3 with respect to the density functional theory benchmark. The chaperone correction leads to ∼10 kcal/mol of additional polarization energy in the product region, bringing the simulated free energy profiles to closer agreement with the experimental results. Furthermore, the solute-solvent radial distribution functions show that the chaperone polarizabilities modify the free energy profiles through enhanced solvation corrections when the system evolves from the charge-neutral reactant state to the charge-separated transition and product states. These results suggest that the dp-QM/MM method, enabled by ML chaperone polarizabilities, provides a very physical remedy for the underpolarization problem in SE/MM-based free energy simulations.

Interligand communication in a metal mediated LL'CT system - a case study.

A series of oxo-Mo(iv) complexes, [MoO(Dt2-)(Dt0)] (where Dt2- = benzene-1,2-dithiol (bdt), toluene-3,4-dithiol (tdt), quinoxaline-2,3-dithiol (qdt), or 3,6-dichloro-benzene-1,2-dithiol (bdtCl2); Dt0 = N,N'-dimethylpiperazine-2,3-dithione (Me2Dt0) or N,N'-diisopropylpiperazine-2,3-dithione ( i Pr2Dt0)), possessing a fully oxidized and a fully reduced dithiolene ligand have been synthesized and characterized. The assigned oxidation states of coordinated dithiolene ligands are supported with spectral and crystallographic data. The molecular structure of [MoO(tdt)( i Pr2Dt0)] (6) demonstrates a large ligand fold angle of 62.6° along the S⋯S vector of the Dt0 ligand. The electronic structure of this system is probed by density functional theory (DFT) calculations. The HOMO is largely localized on the Dt2- ligand while virtual orbitals are mostly Mo and Dt0 in character. Modeling the electronic spectrum of 6 with time dependent (TD) DFT calculations attributes the intense low energy transition at ∼18 000 cm-1 to a ligand-to-ligand charge transfer (LL'CT). The electron density difference map (EDDM) for the low energy transition depicts the electron rich Dt2- ligand donating charge density to the redox-active orbitals of the electron deficient Dt0 ligand. Electronic communication between dithiolene ligands is facilitated by a Mo-monooxo center and distortion about its primary coordination sphere.