Prediction of stability constants of metal-ligand complexes by machine learning for the design of ligands with optimal metal ion selectivity.

The new LOGKPREDICT program integrates HostDesigner molecular design software with the machine learning (ML) program Chemprop. By supplying HostDesigner with predicted log K values, LOGKPREDICT enhances the computer-aided molecular design process by ranking ligands directly by metal-ligand binding strength. Harnessing reliable experimental data from a historic National Institute of Standards and Technology (NIST) database and data from the International Union of Pure and Applied Chemistry (IUPAC), we train message passing neural net algorithms. The multi-metal NIST-based ML model has a root mean square error (RMSE) of 0.629 ± 0.044 (R2 of 0.960 ± 0.006), while two versions of lanthanide-only IUPAC-based ML models have, respectively, RMSE of 0.764 ± 0.073 (R2 of 0.976 ± 0.005) and 0.757 ± 0.071 (R2 of 0.959 ± 0.007). For relative log K predictions on an out-of-sample set of six ligands, demonstrating metal ion selectivity, the RMSE value reaches a commendably low 0.25. We showcase the use of LOGKPREDICT in identifying ligands with high selectivity for lanthanides in aqueous solutions, a finding supported by recent experimental evidence. We also predict new ligands yet to be verified experimentally. Therefore, our ML models implemented through LOGKPREDICT and interfaced with the ligand design software HostDesigner pave the way for designing new ligands with predetermined selectivity for competing metal ions in an aqueous solution.

The General Atomic and Molecular Electronic Structure System (GAMESS): Novel Methods on Novel Architectures.

The primary focus of GAMESS over the last 5 years has been the development of new high-performance codes that are able to take effective and efficient advantage of the most advanced computer architectures, both CPU and accelerators. These efforts include employing density fitting and fragmentation methods to reduce the high scaling of well-correlated (e.g., coupled-cluster) methods as well as developing novel codes that can take optimal advantage of graphical processing units and other modern accelerators. Because accurate wave functions can be very complex, an important new functionality in GAMESS is the quasi-atomic orbital analysis, an unbiased approach to the understanding of covalent bonds embedded in the wave function. Best practices for the maintenance and distribution of GAMESS are also discussed.

Recent developments in the general atomic and molecular electronic structure system.

A discussion of many of the recently implemented features of GAMESS (General Atomic and Molecular Electronic Structure System) and LibCChem (the C++ CPU/GPU library associated with GAMESS) is presented. These features include fragmentation methods such as the fragment molecular orbital, effective fragment potential and effective fragment molecular orbital methods, hybrid MPI/OpenMP approaches to Hartree-Fock, and resolution of the identity second order perturbation theory. Many new coupled cluster theory methods have been implemented in GAMESS, as have multiple levels of density functional/tight binding theory. The role of accelerators, especially graphical processing units, is discussed in the context of the new features of LibCChem, as it is the associated problem of power consumption as the power of computers increases dramatically. The process by which a complex program suite such as GAMESS is maintained and developed is considered. Future developments are briefly summarized.

ParFit: A Python-Based Object-Oriented Program for Fitting Molecular Mechanics Parameters to ab Initio Data.

A newly created object-oriented program for automating the process of fitting molecular-mechanics parameters to ab initio data, termed ParFit, is presented. ParFit uses a hybrid of deterministic and stochastic genetic algorithms. ParFit can simultaneously handle several molecular-mechanics parameters in multiple molecules and can also apply symmetric and antisymmetric constraints on the optimized parameters. The simultaneous handling of several molecules enhances the transferability of the fitted parameters. ParFit is written in Python, uses a rich set of standard and nonstandard Python libraries, and can be run in parallel on multicore computer systems. As an example, a series of phosphine oxides, important for metal extraction chemistry, are parametrized using ParFit. ParFit is in an open source program available for free on GitHub ( https://github.com/fzahari/ParFit ).

Properties of Augmented Kohn-Sham Potential for Energy as Simple Sum of Orbital Energies.

A recent modification to the traditional Kohn-Sham method ( Levy , M. ; Zahariev , F. Phys. Rev. Lett. 2014 , 113 , 113002 ; Levy , M. ; Zahariev , F. Mol. Phys. 2016 , 114 , 1162 - 1164 ), which gives the ground-state energy as a direct sum of the occupied orbital energies, is discussed and its properties are numerically illustrated on representative atoms and ions. It is observed that current approximate density functionals tend to give surprisingly small errors for the highest occupied orbital energies that are obtained with the augmented potential. The appropriately shifted Kohn-Sham potential is the basic object within this direct-energy Kohn-Sham method and needs to be approximated. To facilitate approximations, several constraints to the augmented Kohn-Sham potential are presented.

Silanol-Assisted Carbinolamine Formation in an Amine-Functionalized Mesoporous Silica Surface: Theoretical Investigation by Fragmentation Methods.

The aldol reaction catalyzed by an amine-substituted mesoporous silica nanoparticle (amine-MSN) surface was investigated using a large molecular cluster model (Si392O958C6NH361) combined with the surface integrated molecular orbital/molecular mechanics (SIMOMM) and fragment molecular orbital (FMO) methods. Three distinct pathways for the carbinolamine formation, the first step of the amine-catalyzed aldol reaction, are proposed and investigated in order to elucidate the role of the silanol environment on the catalytic capability of the amine-MSN material. The computational study reveals that the most likely mechanism involves the silanol groups actively participating in the reaction, forming and breaking covalent bonds in the carbinolamine step. Therefore, the active participation of MSN silanol groups in the reaction mechanism leads to a significant reduction in the overall energy barrier for the carbinolamine formation. In addition, a comparison between the findings using a minimal cluster model and the Si392O958C6NH361 cluster suggests that the use of larger models is important when heterogeneous catalysis problems are the target.

Conformations of Organophosphine Oxides.

The conformations of a series of organophosphine oxides, OP(CH3)2R, where R = methyl, ethyl, isopropyl, tert-butyl, vinyl, and phenyl, are predicted using the MP2/cc-pVTZ level of theory. Comparison of potential energy surfaces for rotation about P-C bonds with crystal structure data reveals a strong correlation between predicted location and energetics of minima and histograms of dihedral angle distributions observed in the solid state. In addition, the most stable conformers are those that minimize the extent of steric repulsion between adjacent rotor substituents, and the torsional barriers tend to increase with the steric bulk of the rotating alkyl group. MM3 force field parameters were adjusted to fit the MP2 results, providing a fast and accurate model for predicting organophosphine oxides shapes-an essential part of understanding the chemistry of these compounds. The predictive power of the modified MM3 model was tested against MP2/cc-pVTZ conformations for triethylphosphine oxide, OP(CH2CH3)3, and triphenylphosphine oxide, OP(Ph)3.

Ultra-fast electron capture by electrosterically-stabilized gold nanoparticles.

Ultra-fast pre-solvated electron capture has been observed for aqueous solutions of room-temperature ionic liquid (RTIL) surface-stabilized gold nanoparticles (AuNPs; ∼9 nm). The extraordinarily large inverse temperature dependent rate constants (k(e)∼ 5 × 10(14) M(-1) s(-1)) measured for the capture of electrons in solution suggest electron capture by the AuNP surface that is on the timescale of, and therefore in competition with, electron solvation and electron-cation recombination reactions. The observed electron transfer rates challenge the conventional notion that radiation induced biological damage would be enhanced in the presence of AuNPs. On the contrary, AuNPs stabilized by non-covalently bonded ligands demonstrate the potential to quench radiation-induced electrons, indicating potential applications in fields ranging from radiation therapy to heterogeneous catalysis.

Analytic second derivative of the energy for density functional theory based on the three-body fragment molecular orbital method.

Analytic second derivatives of the energy with respect to nuclear coordinates have been developed for spin restricted density functional theory (DFT) based on the fragment molecular orbital method (FMO). The derivations were carried out for the three-body expansion (FMO3), and the two-body expressions can be obtained by neglecting the three-body corrections. Also, the restricted Hartree-Fock (RHF) Hessian for FMO3 can be obtained by neglecting the density-functional related terms. In both the FMO-RHF and FMO-DFT Hessians, certain terms with small magnitudes are neglected for computational efficiency. The accuracy of the FMO-DFT Hessian in terms of the Gibbs free energy is evaluated for a set of polypeptides and water clusters and found to be within 1 kcal/mol of the corresponding full (non-fragmented) ab initio calculation. The FMO-DFT method is also applied to transition states in SN2 reactions and for the computation of the IR and Raman spectra of a small Trp-cage protein (PDB: 1L2Y). Some computational timing analysis is also presented.

Combined fragment molecular orbital cluster in molecule approach to massively parallel electron correlation calculations for large systems.

The local correlation "cluster-in-molecule" (CIM) method is combined with the fragment molecular orbital (FMO) method, providing a flexible, massively parallel, and near-linear scaling approach to the calculation of electron correlation energies for large molecular systems. Although the computational scaling of the CIM algorithm is already formally linear, previous knowledge of the Hartree-Fock (HF) reference wave function and subsequent localized orbitals is required; therefore, extending the CIM method to arbitrarily large systems requires the aid of low-scaling/linear-scaling approaches to HF and orbital localization. Through fragmentation, the combined FMO-CIM method linearizes the scaling, with respect to system size, of the HF reference and orbital localization calculations, achieving near-linear scaling at both the reference and electron correlation levels. For the 20-residue alanine α helix, the preliminary implementation of the FMO-CIM method captures 99.6% of the MP2 correlation energy, requiring 21% of the MP2 wall time. The new method is also applied to solvated adamantine to illustrate the multilevel capability of the FMO-CIM method.

Ground-state energy as a simple sum of orbital energies in Kohn-Sham theory: a shift in perspective through a shift in potential.

It is observed that the exact interacting ground-state electronic energy of interest may be obtained directly, in principle, as a simple sum of orbital energies when a universal density-dependent term is added to w([ρ];r), the familiar Hartree plus exchange-correlation component in the Kohn-Sham effective potential. The resultant shifted potential, w[over ¯]([ρ];r), actually changes less on average than w([ρ];r) when the density changes, including the fact that w[over ¯]([ρ];r) does not undergo a discontinuity when the number of electrons increases through an integer. Thus, the approximation of w[over ¯]([ρ];r) represents an alternative direct approach for the approximation of the ground-state energy and density.

Dynamics simulations with spin-flip time-dependent density functional theory: photoisomerization and photocyclization mechanisms of cis-stilbene in ππ* states.

On-the-fly dynamics simulations were carried out using spin-flip time dependent density functional theory (SF-TDDFT) to examine the photoisomerization and photocyclization mechanisms of cis-stilbene following excitation to the ππ* state. A state tracking method was devised to follow the target state among nearly degenerate electronic states during the dynamics simulations. The steepest descent path from the Franck-Condon structure of cis-stilbene in the ππ* state is shown to reach the S1-minimum of 4,4-dihydrophenanthrene (DHP) via a cis-stilbene-like structure (referred to as (S1)cis-min) on a very flat region of the S1-potential energy surface. From the dynamics simulations, the branching ratio of the photoisomerization is calculated as trans:DHP = 35:13, in very good agreement with the experimental data, trans:DHP = 35:10. The discrepancy between the steepest descent pathway and the significant trans-stilbene presence in the branching ratio observed experimentally and herein computationally is clarified from an analysis of geometrical features along the reaction pathway, as well as the low barrier of 0.1 eV for the pathway from (S1)cis-min to the twisted pyramidal structure on the S1-potential energy surface. It is concluded that ππ*-excited cis-stilbene propagates primarily toward the twisted structural region due to dynamic effects, with partial branching to the DHP structural region via the flat-surface region around (S1)cis-min.

Nonlinear response time-dependent density functional theory combined with the effective fragment potential method.

This work presents an extension of the linear response TDDFT/EFP method to the nonlinear-response regime together with the implementation of nonlinear-response TDDFT/EFP in the quantum-chemistry computer package GAMESS. Included in the new method is the ability to calculate the two-photon absorption cross section and to incorporate solvent effects via the EFP method. The nonlinear-response TDDFT/EFP method is able to make correct qualitative predictions for both gas phase values and aqueous solvent shifts of several important nonlinear properties.

The R(-7) Dispersion Interaction in the General Effective Fragment Potential Method.

The R(-7) term (E7) in the dispersion expansion is developed in the framework of the general effective fragment potential (EFP2) method, formulated with the dynamic anisotropic Cartesian polarizability tensors over the imaginary frequency range. The E7 formulation is presented in terms of both the total molecular polarizability and the localized molecular orbital (LMO) contributions. An origin transformation from the center of mass to the LMO centroids is incorporated for the computation of the LMO dipole-quadrupole polarizability. The two forms considered for the damping function for the R(-7) dispersion interaction, the overlap-based and Tang-Toennies damping functions, are extensions of the existing damping functions for the R(-6) term in the dispersion expansion. The R(-7) dispersion interaction is highly orientation dependent: it can be either attractive or repulsive, and its magnitude can change substantially as the relative orientation of two interacting molecules changes. Although the R(-7) dispersion energy rotationally averages to zero, it may be significant for systems in which rotational averaging does not occur, such as rotationally rigid molecular systems as in molecular solids or constrained surface reactions.

Analytic Gradient for Density Functional Theory Based on the Fragment Molecular Orbital Method.

The equations for the response terms for the fragment molecular orbital (FMO) method interfaced with the density functional theory (DFT) gradient are derived and implemented. Compared to the previous FMO-DFT gradient, which lacks response terms, the FMO-DFT analytic gradient has improved accuracy for a variety of functionals, when compared to numerical gradients. The FMO-DFT gradient agrees with the fully ab initio DFT gradient in which no fragmentation is performed, while reducing the nonlinear scaling associated with standard DFT. Solving for the response terms requires the solution of the coupled perturbed Kohn-Sham (CPKS) equations, where the CPKS equations are solved through a decoupled Z-vector procedure called the self-consistent Z-vector method. FMO-DFT is a nonvariational method and the FMO-DFT gradient is unique compared to standard DFT gradients in that the FMO-DFT gradient requires terms from both DFT and time-dependent density functional theory (TDDFT) theories.

Benchmarking the performance of time-dependent density functional methods.

The performance of 24 density functionals, including 14 meta-generalized gradient approximation (mGGA) functionals, is assessed for the calculation of vertical excitation energies against an experimental benchmark set comprising 14 small- to medium-sized compounds with 101 total excited states. The experimental benchmark set consists of singlet, triplet, valence, and Rydberg excited states. The global-hybrid (GH) version of the Perdew-Burke-Ernzerhoff GGA density functional (PBE0) is found to offer the best overall performance with a mean absolute error (MAE) of 0.28 eV. The GH-mGGA Minnesota 2006 density functional with 54% Hartree-Fock exchange (M06-2X) gives a lower MAE of 0.26 eV, but this functional encounters some convergence problems in the ground state. The local density approximation functional consisting of the Slater exchange and Volk-Wilk-Nusair correlation functional (SVWN) outperformed all non-GH GGAs tested. The best pure density functional performance is obtained with the local version of the Minnesota 2006 mGGA density functional (M06-L) with an MAE of 0.41 eV.

Solvent-induced shift of the lowest singlet π → π* charge-transfer excited state of p-nitroaniline in water: an application of the TDDFT/EFP1 method.

The combined time-dependent density functional theory effective fragment potential method (TDDFT/EFP1) is applied to a study of the solvent-induced shift of the lowest singlet π → π* charge-transfer excited state of p-nitroaniline (pNA) from the gas to the condensed phase in water. Molecular dynamics simulations of pNA with 150 EFP1 water molecules are used to model the condensed-phase and generate a simulated spectrum of the lowest singlet charge-transfer excitation. The TDDFT/EFP1 method successfully reproduces the experimental condensed-phase π → π* vertical excitation energy and solvent-induced red shift of pNA in water. The largest contribution to the red shift comes from Coulomb interactions, between pNA and water, and solute relaxation. The solvent shift contributions reflect the increase in zwitterionic character of pNA upon solvation.

Implementation of the analytic energy gradient for the combined time-dependent density functional theory/effective fragment potential method: application to excited-state molecular dynamics simulations.

Excited-state quantum mechanics/molecular mechanics molecular dynamics simulations are performed, to examine the solvent effects on the fluorescence spectra of aqueous formaldehyde. For that purpose, the analytical energy gradient has been derived and implemented for the linear-response time-dependent density functional theory (TDDFT) combined with the effective fragment potential (EFP) method. The EFP method is an efficient ab initio based polarizable model that describes the explicit solvent effects on electronic excitations, in the present work within a hybrid TDDFT/EFP scheme. The new method is applied to the excited-state MD of aqueous formaldehyde in the n-π* state. The calculated π*→n transition energy and solvatochromic shift are in good agreement with other theoretical results.

A paradigm for blue- or red-shifted absorption of small molecules depending on the site of π-extension.

Benzannulation of aromatic molecules is often used to red-shift absorption and emission bands of organic and inorganic, molecular, and polymeric materials; however, in some cases, either red or blue shifts are observed, depending on the site of benzannulation. A series of five platinum(II) complexes of the form (N(∧)N(∧)N)PtCl are reported here that illustrate this phenomenon, where N(∧)N(∧)N represents the tridentate monoanionic ligands 2,5-bis(2-pyridylimino)3,4-diethylpyrrolate (1), 1,3-bis(2-pyridylimino)isoindolate (2), 1,3-bis(2-pyridylimino)benz(f)isoindolate (3), 1,3-bis(2-pyridylimino)benz(e)isoindolate (4), and 1,3-bis(1-isoquinolylimino) isoindolate (5). For this series of molecules, either a blue shift (2 and 3) or a red shift (4 and 5) in absorption and emission maxima, relative to their respective nonbenzannulated compounds, was observed that depends on the site of benzannulation. Experimental data and first principles calculations suggest that a similar HOMO energy level and a destabilized or stabilized LUMO with benzannulation is responsible for the observed trends. A rationale for LUMO stabilization/destabilization is presented using simple molecular orbital theory. This explanation is expanded to describe other molecules with this unusual behavior.

Solvent effects on optical properties of molecules: a combined time-dependent density functional theory/effective fragment potential approach.

A quantum mechanics/molecular mechanics (QM/MM) type of scheme is employed to calculate the solvent-induced shifts of molecular electronic excitations. The effective fragment potential (EFP) method was used for the classical potential. Since EFP has a density dependent functional form, in contrast with most other MM potentials, time-dependent density functional theory (TDDFT) has been modified to combine TDDFT with EFP. This new method is then used to perform a hybrid QM/MM molecular dynamics simulation to generate a simulated spectrum of the n-->pi(*) vertical excitation energy of acetone in vacuum and with 100 water molecules. The calculated water solvent effect on the vertical excitation energy exhibits a blueshift of the n-->pi(*) vertical excitation energy in acetone (Delta omega(1)=0.211 eV), which is in good agreement with the experimental blueshift.