Assessment of Methodology and Chemical Group Dependences in the Calculation of the p<i>K</i>_a for Several Chemical Groups

We have investigated the dependencies of various computational methods in the calculation of acid dissociation constants (p<i>K</i>_a values) of certain chemical groups found in protonatable amino acids based on our previous scheme [Matsui; Phys. Chem. Chem. Phys. 2012, 14, 4181−4187]. By changing the quantum chemical (QC) method (Hartree–Fock (HF) and perturbation theory, and composite methods, or exchange–correlation functionals in density functional theory (DFT)), basis sets, solvation models, and the cavities used in the solvent models, we have exhaustively tested about 2,200 combinations to find the best combination for p<i>K</i>_a estimation among them. Of the tested parameters, the choice of the basis set and cavity is the most crucial to reproduce experimental values compared to other factors. Concerning the basis set, the inclusion of diffuse functions is quite important for carboxyl, thiol, and phenol groups judging from the mean absolute errors (MAEs) measured from the experimental values. Of the cavity models, between the Pauling, Klamt, and the universal force field (UFF) definitions, the UFF defined cavity is the best choice, resulting in the smallest MAEs. Concerning the QC methods, hybrid DFTs and range-separated DFTs always provide better results than pure DFTs and HF. As a result, we found that LC-ϖPBE/6-31+G­(d) with PCM-SMD/UFF provides the best p<i>K</i>_a estimation with a MAE within 0.15 p<i>K</i>_a units

Theoretical Insight into Stereoselective Reaction Mechanisms of 2,4-Pentanediol-Tethered Ketene-Olefin [2 + 2] Cycloaddition

We report ab initio molecular dynamics calculations based on density functional theory performed on an intramolecular [2 + 2] cycloaddition between ketene and olefin linked with a 2,4-pentanediol (PD) tether. We find that the encounter of the ketene and olefin moieties could be prearranged in the thermal equilibrated state before the cycloaddition. The reaction mechanism is found to be stepwise, similar to that of intermolecular ketene [2 + 2] cycloadditions with ordinary alkenes. A distinct feature of the reaction pathway for a major diastereoisomer is a differential activation free energy of about 1.5 kcal/mol, including 2.8 kcal/mol as the differential activation entropy, with a transition state consisting of a flexible nine-membered ring in the olefin-PD-ketene moiety. This theoretical study provides a reasonable explanation for the strict stereocontrollability of the PD-tethered ketene-olefin cycloaddition, irrespective of reaction types or conditions

A Density Functional Theory Based Protocol to Compute the Redox Potential of Transition Metal Complex with the Correction of Pseudo-Counterion: General Theory and Applications

We propose an accurate scheme to evaluate the redox potential of a wide variety of transition metal complexes by adding a charge-dependent correction term for a counterion around the charged complexes, which is based on Generalized Born theory, to the solvation energy. The mean absolute error (MAE) toward experimental redox potentials of charged complexes is considerably reduced from 0.81 V (maximum error 1.22 V) to 0.22 V (maximum error 0.50 V). We found a remarkable exchange-correlation functional dependence on the results rather than the basis set ones. The combination of Wachters+f (for metal) and 6-31++G­(d,p) (for other atoms) with the B3LYP functional gives the least MAE 0.15 V for the test complexes. This scheme is applicable to other solvents, and heavier transition metal complexes such as M₁(CO)₅(pycn) (M₁ = Cr, Mo, W), M₂(mnt)₂ (M₂ = Ni, Pd, Pt), and M₃(bpy)₃ (M₃ = Fe, Ru, Os) with the same quality

Molecular Dynamics and Quantum Chemical Approach for the Estimation of an Intramolecular Hydrogen Bond Strength in Okadaic Acid

We have evaluated the strength of intramolecular hydrogen bond in a protein based on molecular dynamics and quantum chemical calculation. To estimate the intramolecular hydrogen bond strength in okadaic acid (OA), we analyzed the influence of solvent and protonation states on the hydrogen bond and the entire structure. We performed molecular dynamics calculation and analyzed the strength of the hydrogen bond by measuring bond length and bond angle. The stable structure differs depending on the kind of solvent used and the protonation state of OA. Using the mean interaction energy from the quantum chemical calculation, hydrogen bond length and angle were investigated against bond energy. Although dielectric constant slightly depends on bond energy, the estimation of the intramolecular hydrogen bond strength in OA is possible even in a protein environment. The Coulomb interaction between OA and surrounding arginine produced a more negatively charged O1 in OA. The hydrogen bond energy in the deprotonated state is larger than that in the protonated state

Analyses of Thiophene-Based Donor–Acceptor Semiconducting Polymers toward Designing Optical and Conductive Properties: A Theoretical Perspective

We theoretically investigated the physical properties, including the frontier orbital and excitation energies, for thiophene-based semiconducting polymers composed of donor and acceptor units. Orbital analysis revealed that remarkably different behaviors of frontier orbital energies with respect to the degree of polymerization stems from the distribution of the frontier orbitals, which is insightful information for controlling the ionization potentials and electron affinities of semiconducting polymers. We also successfully estimated the frontier orbital energies of the polymers through a simple Hückel theory-based analytical model parametrized from calculations of relatively small oligomers. This simple model allows us to predict the highest occupied molecular orbital–lowest unoccupied molecular orbital gaps of a polymer at a low computational cost. The simulated absorption spectra of the thiophene-based semiconducting polymers were compared with the experimental spectra. The theoretically designed polymers were also investigated in terms of their frontier orbital energies and absorption spectra toward synthesizing promising polymers

How Can We Understand Au₈ Cores and Entangled Ligands of Selenolate- and Thiolate-Protected Gold Nanoclusters Au₂₄(ER)₂₀ and Au₂₀(ER)₁₆ (E = Se, S; R = Ph, Me)? A Theoretical Study

The geometries and electronic structures of selenolate-protected Au nanoclusters, Au₂₄(SeR)₂₀ and Au₂₀(SeR)₁₆, and their thiolate analogues are theoretically investigated with DFT and SCS-MP2 methods, to elucidate the electronic structure of their unusual Au₈ core and the reason why they have the unusual entangled “staple-like” chain ligands. The Au₈ core is understood to be an [Au₄]²⁺ dimer in which the [Au₄]²⁺ species has a tetrahedral geometry with a closed-shell singlet ground state. The SCS-MP2 method successfully reproduced the distance between two [Au₄]²⁺ moieties, but the DFT with various functionals failed it, suggesting that the dispersion interaction is crucial between these two [Au₄]²⁺ moieties. The SCS-MP2-calculated formation energies of these nanocluster compounds indicate that the thiolate staple-like chain ligands are more stable than the selenolate ones, but the Au₈ core more strongly coordinates with the selenolate staple-like chain ligands than with the thiolate ones. Though Au₂₀(SeR)₁₆ has not been reported yet, its formation energy is calculated to be large, suggesting that this compound can be synthesized as a stable species if the concentration of Au­(SeR) is well adjusted. The aurophilic interactions between the staple-like chain ligands and between the Au₈ core and the staple-like chain ligand play an important role for the stability of these compounds. Because of the presence of this autophilic interaction, Au₂₄(SeR)₂₀ is more stable than Au₂₀(SeR)₁₆ and the unusual entangled ligands are involved in these compounds

Koopmans’ Theorem-Compliant Long-Range Corrected (KTLC) Density Functional Mediated by Black-Box Optimization and Data-Driven Prediction for Organic Molecules

Density functional theory (DFT) is a significant computational tool that has substantially influenced chemistry, physics, and materials science. DFT necessitates parametrized approximation for determining an expected value. Hence, to predict the properties of a given molecule using DFT, appropriate parameters of the functional should be set for each molecule. Herein, we optimize the parameters of range-separated functionals (LC-BLYP and CAM-B3LYP) via Bayesian optimization (BO) to satisfy Koopmans’ theorem. Our results demonstrate the effectiveness of the BO in optimizing functional parameters. Particularly, Koopmans’ theorem-compliant LC-BLYP (KTLC-BLYP) shows results comparable to the experimental UV-absorption values. Furthermore, we prepared an optimized parameter dataset of KTLC-BLYP for over 3000 molecules through BO for satisfying Koopmans’ theorem. We have developed a machine learning model on this dataset to predict the parameters of the LC-BLYP functional for a given molecule. The prediction model automatically predicts the appropriate parameters for a given molecule and calculates the corresponding values. The approach in this paper would be useful to develop new functionals and to update the previously developed functionals

Koopmans’ Theorem-Compliant Long-Range Corrected (KTLC) Density Functional Mediated by Black-Box Optimization and Data-Driven Prediction for Organic Molecules

Density functional theory (DFT) is a significant computational tool that has substantially influenced chemistry, physics, and materials science. DFT necessitates parametrized approximation for determining an expected value. Hence, to predict the properties of a given molecule using DFT, appropriate parameters of the functional should be set for each molecule. Herein, we optimize the parameters of range-separated functionals (LC-BLYP and CAM-B3LYP) via Bayesian optimization (BO) to satisfy Koopmans’ theorem. Our results demonstrate the effectiveness of the BO in optimizing functional parameters. Particularly, Koopmans’ theorem-compliant LC-BLYP (KTLC-BLYP) shows results comparable to the experimental UV-absorption values. Furthermore, we prepared an optimized parameter dataset of KTLC-BLYP for over 3000 molecules through BO for satisfying Koopmans’ theorem. We have developed a machine learning model on this dataset to predict the parameters of the LC-BLYP functional for a given molecule. The prediction model automatically predicts the appropriate parameters for a given molecule and calculates the corresponding values. The approach in this paper would be useful to develop new functionals and to update the previously developed functionals