Evaluation Procedure of Electrostatic Potential in 3D-RISM-SCF Method and Its Application to Hydrolyses of Cis- and Transplatin Complexes

In the three-dimensional reference interaction site model self-consistent field (3D-RISM-SCF) method, a switching function was introduced to evaluate the electrostatic potential (ESP) around the solute to smoothly connect the ESP directly calculated with the solute electronic wave function and that approximately calculated with solute point charges. Hydrolyses of cis- and transplatins, <i>cis</i>- and <i>trans</i>-PtCl₂(NH₃)₂, were investigated with this method. Solute geometries were optimized at the DFT level with the M06-2X functional, and free energy changes were calculated at the CCSD­(T) level. In the first hydrolysis, the calculated activation free energy is 20.8 kcal/mol for cisplatin and 20.3 kcal/mol for transplatin, which agrees with the experimental and recently reported theoretical results. A Cl anion, which is formed by the first hydrolysis, somehow favorably exists in the first solvation shell as a counteranion. The second hydrolysis occurs with a similar activation free energy (20.9 kcal/mol) for cisplatin but a somewhat larger energy (23.2 kcal/mol) for transplatin to afford <i>cis</i>- and <i>trans</i>-diaqua complexes. The Cl counteranion in the first solvation shell little influences the activation free energy but somewhat decreases the endothermicity in both cis- and transplatins. The present 3D-RISM-SCF method clearly displays the microscopic solvation structure and its changes in the hydrolysis, which are discussed in detail

3D-RISM-MP2 Approach to Hydration Structure of Pt(II) and Pd(II) Complexes: Unusual H‑Ahead Mode vs Usual O‑Ahead One

Solvation of transition metal complexes with water has been one of the fundamental topics in physical and coordination chemistry. In particular, Pt­(II) complexes have recently attracted considerable interest for their relation to anticancer activity in cisplatin and its analogues, yet the interaction of the water molecule and the metal center has been obscured. The challenge from a theoretical perspective remains that both the microscopic solvation effect and the dynamical electron correlation (DEC) effect have to be treated simultaneously in a reasonable manner. In this work we derive the analytical gradient for the three-dimensional reference interaction site model Møller–Plesset second order (3D-RISM-MP2) free energy. On the basis of the three-regions 3D-RISM self-consistent field (SCF) method recently proposed by us, we apply a new layer of the Z-vector method to the CP-RISM equation as well as point-charge approximation to the derivatives with respect to the density matrix elements in the RISM-CPHF equation to remarkably reduce the computational cost. This method is applied to study the interaction of H₂O with the d⁸ square planar transition metal complexes in aqueous solution, trans-[Pt^IICl₂(NH₃)­(glycine)] (<b>1a</b>), [Pt^II(NH₃)₄]²⁺ (<b>1b</b>), [Pt^II(CN)₄]^2– (<b>1c</b>), and their Pd­(II) analogues <b>2a</b>, <b>2b</b>, and <b>2c</b>, respectively, to elucidate whether the usual H₂O interaction through O atom (O-ahead mode) or unusual one through H atom (H-ahead mode) is stable in these complexes. We find that the interaction energy of the coordinating water and the transition metal complex changes little when switching from gas to aqueous phase, but the solvation free energy differs remarkably between the two interaction modes, thereby affecting the relative stability of the H-ahead and O-ahead modes. Particularly, in contrast to the expectation that the O-ahead mode is preferred due to the presence of positive charges in <b>1b</b>, the H-ahead mode is also found to be more stable. The O-ahead mode is found to be more stable than the H-ahead one only in <b>2b</b>. The energy decomposition analysis (EDA) at the 3D-RISM-MP2 level revealed that the O-ahead mode is stabilized by the electrostatic (ES) interaction, whereas the H-ahead one is mainly stabilized by the DEC effect. The ES interaction is also responsible for the difference between the Pd­(II) and Pt­(II) complexes; because the electrostatic potential is more negative along the <i>z</i>-axis in the Pt­(II) complex than in the Pd­(II) one, the O-ahead mode prefers the Pd­(II) complexes, whereas the H-ahead becomes predominant in the Pt­(II) complexes

Like-Charge Attraction of Molecular Cations in Water: Subtle Balance between Interionic Interactions and Ionic Solvation Effect

Despite strong electrostatic repulsion, like-charged ions in aqueous solution can effectively attract each other via ion–water interactions. In this paper we investigate such an effective interaction of like-charged ions in water by using the 3D-RISM-SCF method (i.e., electronic structure theory combined with three-dimensional integral equation theory for molecular solvents). Free energy profiles are calculated at the CCSD­(T) level for a series of molecular ions including guanidinium (Gdm⁺), alkyl-substituted ammonium, and aromatic amine cations. Polarizable continuum model (PCM) and mean-field QM/MM free energy calculations are also performed for comparison. The results show that the stability of like-charged ion pairs in aqueous solution is determined by a very subtle balance between interionic interactions (including dispersion and π-stacking interactions) and ionic solvation/hydrophobic effects and that the Gdm⁺ ion has a rather favorable character for like-charge association among all the cations studied. Furthermore, we investigate the like-charge pairing in Arg-Ala-Arg and Lys-Ala-Lys tripeptides in water and show that the Arg-Arg pair has a contact free-energy minimum of about −6 kcal/mol. This result indicates that arginine pairing observed on protein surfaces and interfaces is stabilized considerably by solvation effects

Theoretical Study of One-Electron Oxidized Mn(III)– and Ni(II)–Salen Complexes: Localized vs Delocalized Ground and Excited States in Solution

One-electron oxidized Mn­(III)– and Ni­(II)–salen complexes exhibit unique mixed-valence electronic structures and charge transfer (CT) absorption spectra. We theoretically investigated them to elucidate the reason why the Mn­(III)–salen complex takes a localized electronic structure (class II mixed valence compound by Robin–Day classification) and the Ni­(II)-analogue has a delocalized one (class III) in solution, where solvation effect was taken into consideration either by the three-dimensional reference interaction site model self-consistent field (3D-RISM-SCF) method or by the mean-field (MF) QM/MM-MD simulation. The geometries of these complexes were optimized by the 3D-RISM-SCF-U-DFT/M06. The vertical excitation energy and the oscillator strength of the first excited state were evaluated by the general multiconfiguration reference quasi-degenerate perturbation theory (GMC-QDPT), including the solvation effect based on either 3D-RISM-SCF- or MF-QM/MM-MD-optimized solvent distribution. The computational results well agree with the experimentally observed absorption spectra and the experimentally proposed electronic structures. The one-electron oxidized Mn­(III)–salen complex with a symmetrical salen ligand belongs to the class II, as experimentally reported, in which the excitation from the phenolate anion to the phenoxyl radical moiety occurs. In contrast, the one-electron oxidized Ni­(II)–salen complex belongs to the class III, in which the excitation occurs from the doubly occupied delocalized π₁ orbital of the salen radical to the singly occupied delocalized π₂ orbital; the π₁ is a bonding combination of the HOMOs of two phenolate moieties and the π₂ is an antibonding combination. Solvation effect is indispensable for correctly describing the mixed-valence character, the geometrical distortion, and the intervalence CT absorption spectra of these complexes. The number of d electrons and the d orbital energy level play crucial roles to provide the localization/delocalization character of these complexes