Interaction Site Model Self-consistent Field Research Articles

Spin-Spin Coupling Constant Based on Reference Interaction Site Model Self-Consistent Field with Constrained Spatial Electron Density.

A method for computing spin-spin coupling constants (SSCCs) using the reference interaction site model self-consistent field with constrained spatial electron density (RISM-SCF-cSED) is proposed for the first time. Describing solvents using integral equation theory allows us to reflect solvent effects at atomic resolution in SSCCs while accounting for thermal fluctuations at a low computational cost. Applying the method to water, 1,1-difluoroethylene, and 1-methylaminomethylene-2-naphthalenone revealed that the solvent shift was evaluated to a greater extent than in the continuum solvent model. The origin of this phenomenon was analyzed in terms of the physical mechanisms underlying SSCCs.

Vibrational Self-Consistent Field (VSCF) and Post-VSCF Method Calculations Combined with the Reference Interaction Site Model Self-Consistent Field Method Coupled with the Constrained Spatial Electron Density Distribution: Applications to NaHCOO in Aqueous Phase.

Investigating vibrational behavior in solution is crucial for understanding molecular dynamics within a solvent environment. Notably, the analysis of Raman spectra for molecules in solution is important owing to its ability to unveil intricate solute-solvent interactions. Previous studies have effectively employed frequency calculations utilizing the reference interaction site model self-consistent field method in conjunction with constrained spatial electron density distribution (RISM-SCF-cSED) to understand molecular vibrations in solution, primarily focusing on fundamental vibrational modes. However, the oversight of overtones and combination tones in these studies prompted us to combine the vibrational self-consistent field (VSCF) and vibrational second-order Mo̷ller-Plesset perturbation (VMP2) methods with RISM-SCF-cSED to address these aspects theoretically. Illustrating the efficacy of this integrated approach, we computed the Raman spectra of sodium formate (NaHCOO) in water, revealing the necessity of accounting for molecular anharmonicity in solution vibrational analysis. Our findings underscore the potency of VSCF and VMP2 in conjunction with RISM-SCF-cSED as a robust theoretical framework for such calculations.

Lagrangian of extended multiconfigurational self-consistent field second-order quasidegenerate perturbation theory combined with reference interaction site model self-consistent field constraint spatial electron density.

Lagrangians of the state-averaged multiconfigurational self-consistent field (SA-MCSCF) and multistate extended second-order quasidegenerate perturbation theory (MS-XMCQDPT2) coupled with the reference interaction site model self-consistent field constraint spatial electron density are defined. In addition, variational equations were derived to calculate the excitation energies of the target molecules dissolved in various solvents. The theory was applied to a phenol molecule in various solutions, and the gradients and Hessian matrices were calculated to evaluate the absorption spectral lines, including the broadening bandwidth. Numerical calculations revealed fine structures in any solvent surroundings. The main intramolecular vibrational modes related to such fine structures were stretching vibrations of the aromatic ring and the oxygen atom of the phenol molecule. The present theory plays an important role in predicting the structure of potential energy surfaces, such as Hessian matrices for various solvent types, during the photoexcitation process.

Solvent Distribution Effects on Quantum Chemical Calculations with Quantum Computers.

We present a combination of three-dimensional reference interaction site model self-consistent field (3D-RISM-SCF) theory and the variational quantum eigensolver (VQE) to consider the solvent distribution effects within the framework of quantum-classical hybrid computing. The present method, 3D-RISM-VQE, does not include any statistical errors from the solvent configuration sampling owing to the analytical treatment of the statistical solvent distribution. We apply 3D-RISM-VQE to compute the spatial distribution functions of solvent water around a water molecule, the potential and Helmholtz energy curves of NaCl, and to analyze the Helmholtz energy component and related properties of H2O and NH4+. Moreover, we utilize 3D-RISM-VQE to analyze the extent to which solvent effects alter the efficiency of quantum calculations compared with calculations in the gas phase using the L1-norms of molecular electronic Hamiltonians. Our results demonstrate that the efficiency of quantum chemical calculations on a quantum computer in solution is virtually the same as that in the gas phase.

Recent developments and applications of reference interaction site model self-consistent field with constrained spatial electron density (RISM-SCF-cSED): A hybrid model of quantum chemistry and integral equation theory of molecular liquids

The significance of solvent effects in electronic structure calculations has long been noted, and various methods have been developed to consider this effect. The reference interaction site model self-consistent field with constrained spatial electron density (RISM-SCF-cSED) is a hybrid model that combines the integral equation theory of molecular liquids with quantum chemistry. This method can consider the statistically convergent solvent distribution at a significantly lower cost than molecular dynamics simulations. Because the RISM theory explicitly considers the solvent structure, it performs well for systems where hydrogen bonds are formed between the solute and solvent molecules, which is a challenge for continuum solvent models. Taking advantage of being founded on the variational principle, theoretical developments have been made in calculating various properties and incorporating electron correlation effects. In this review, we organize the theoretical aspects of RISM-SCF-cSED and its distinctions from other hybrid methods involving integral equation theories. Furthermore, we carefully present its progress in terms of theoretical developments and recent applications.

Theoretical Study of Raman Intensities of p-Nitroaniline in Different Solvent Conditions by Using a Reference Interaction Site Model Self-Consistent Field Explicitly Including Constrained Spatial Electron Density Distribution.

Raman spectroscopy is one of the most powerful tools to understand and characterize the states and structures of systems in several environments. To obtain highly accurate changes in Raman intensities of systems in solution, theoretical treatment, which can deal with not only the states and structures of systems but also the environment around molecules, proves to be significant. Hence, in this study, we developed the calculation of changes in Raman intensities of systems in different solvent conditions by using the reference interaction site model self-consistent field study explicitly including constrained spatial electron density distribution; this model is designed based on elements from both quantum mechanics and statistical mechanics. We showed that our calculation method could reproduce the changes in Raman intensities of p-nitroaniline (pNA) under different solvent conditions, including supercritical water, which has been observed in previous experimental studies. Based on the analysis of the calculation results, we observed that the ratio of the Raman intensity change of pNA in different solvent conditions is strongly correlated with the charge-transfer character of pNA.

Application of the reference interaction site model self-consistent field method based on the Dirac-Hartree–Fock wave function to a chemical reaction

The reference interaction site model self-consistent field (RISM-SCF) method is a combined method of the electronic structure theory of molecules and the integral equation theory of molecular liquids. The RISM-SCF method based on the Dirac-Hartree-Fock wave function, recently proposed, is applied to a chemical reaction, specifically, a Menshutkin reaction in aqueous solution. The Helmholtz energy profile along the reaction coordinate is calculated and the characteristics of the reaction are discussed based on energy component analysis.

Reference interaction site model self-consistent field with constrained spatial electron density approach for nuclear magnetic shielding in solution.

We propose a new hybrid approach combining quantum chemistry and statistical mechanics of liquids for calculating the nuclear magnetic resonance (NMR) chemical shifts of solvated molecules. Based on the reference interaction site model self-consistent field with constrained spatial electron density distribution (RISM-SCF-cSED) method, the electronic structure of molecules in solution is obtained, and the expression for the nuclear magnetic shielding tensor is derived as the second-order derivative of the Helmholtz energy of the solution system. We implemented a method for calculating chemical shifts and applied it to an adenine molecule in water, where hydrogen bonding plays a crucial role in electronic and solvation structures. We also performed the calculations of 17O chemical shifts, which showed remarkable solvent dependence. While converged results could not be sometimes obtained using the conventional method, in the present framework with RISM-SCF-cSED, an adequate representation of electron density is guaranteed, making it possible to obtain an NMR shielding constant stably. This introduction of cSED is key to extending the method's applicability to obtain the chemical shift of various chemical species. The present demonstration illustrates our approach's superiority in terms of numerical robustness and accuracy.

Spin-Orbit Coupling Calculation Combined with the Reference Interaction Site Model Self-Consistent Field Explicitly Including Constrained Spatial Electron Density Distribution.

Studying the radiative and non-radiative decay processes of molecules in a solution is an important issue in the design of organic and functional molecules. Theoretical approaches have great potential for revealing this decay process through computation of various parameters, such as the energy surfaces at the excited state and spin-orbit coupling (SOC). The development of quantum chemical programs has enabled the calculation of SOC values to become popular for the gas phase. However, SOC calculations in solution have some difficulties that need to be overcome. In the present study, the authors combined the SOC calculations with the reference interaction site model self-consistent field explicitly including constrained spatial electron density distribution. To validate the reliability of our method, the decay process of dimethylaminobenzonitrile in cyclohexane and acetonitrile was studied. By computing the SOC values in both solution systems, the authors were able to investigate the decay process at the atomistic level. Furthermore, a natural transition orbital analysis and the measurement of the decomposed SOC values were found to provide a clear understanding of intersystem crossing.

Investigation of the metastable structures of polyiodide in acetonitrile studied using global reaction route mapping and the reference interaction site model self-consistent field explicitly including constrained spatial electron density distribution.

In this study, we theoretically analyzed the metastable structures of polyiodide (I7-) in the gas and acetonitrile phases using global reaction route mapping and the reference interaction site model self-consistent field explicitly including constrained spatial electron density distribution. From the chemical reaction pathways of I7- in acetonitrile, it was found that there would be 2 types of isomerization pathways. One proceeds with constant stoichiometry and the other takes place by breaking and forming I-I bonds. In addition, we discovered that I7- had various metastable structures within ∼10 kcal mol-1. Comparing the most stable structure in the gas and acetonitrile phases, the tetrapot type is found to be the most stable structure in the gas phase; however, it is the zigzag type in acetonitrile. In order to understand this difference, we performed the decomposition analysis of the thermal correlation term in the gas and acetonitrile phases. It was found that thermal correction plays a key role in the stability and we could explain the difference in the population of the EQ states of I7- in each phase. Overall, we revealed that the solvation effect must be one of the crucial factors to stabilize the isomers of I7- and determine the chemical reaction pathways.

Solvation in nitration of benzene and the valence electronic structure of the Wheland intermediate.

Nitration of benzene is a representative aromatic substitution reaction related to the σ-complex (arenium ion or "Wheland" intermediate) concept. This reaction is typically carried out in a mixed acid solution to generate nitronium ions, and how solvent molecules play roles in the reaction has been of great interest. Here we will shed new light on the reaction, namely the electronic structure and the microscopic insights of the solvation, which have been rarely discussed so far. We studied this process using the reference interaction site model-self consistent field with constrained spatial electron density distribution (RISM-SCF-cSED) method, considering sulfuric acid or water molecules as a solvent. In this method, the electronic structure of the solute and the solvation structure are self-consistently determined based on quantum chemistry and statistical mechanics of molecular liquids. The solvation free energy surfaces in solution and solvation structures were verified. In the bond formation process of benzene and nitronium ions, the solvation structure by sulfuric acid molecules drastically changes and the solvation effect on the free energy is quite large. We revealed largely contributing resonance structures in the π-electron system of the σ-complex in gas and solution phases by analysing the valence electronic structures.

Analytical second derivatives of the free energy in solution by the reference interaction site model self-consistent field explicitly including constrained spatial electron density distribution

The application of analytical derivative methods to solution systems is important because several chemical reactions occur in solution. The reference interaction site model (RISM) is one of the solvation theories used to study solution systems and has shown good performance, especially in the polar solvent systems. Although the analytical first derivative based on the RISM coupled with quantum methods (RISM-SCF) has already been derived, the analytical second derivative has not been proposed yet. Therefore, in this study, the analytical second derivative was derived using RISM-SCF explicitly including constrained spatial electron density distribution (RISM-SCF-cSED). The performance of this method was validated with the Hessian calculations of formaldehyde and para-nitroaniline in solution, and the results demonstrated that the method accurately calculated frequency values at a small computational cost.

Accurate Absorption Energy Calculations in Solution Using the Reference Interaction Site Model Self-Consistent Field Including the Constrained Spatial Electron Density Distribution

The solvation effect is an important factor determining the properties of molecules in solution. The reference interaction site model (RISM) is a powerful method to treat the solvation effect with pair-correlation functions, such as a radial distribution function. This study developed a hybrid method between quantum mechanics and RISM using the spatial electron density distributions on each atomic site (RISM-SCF-cSED). Sophisticated quantum mechanical approaches can be used to consider the solvation effect because the computational cost of RISM-SCF-cSED is reasonable. In this study, the absorption energies of 5-(dimethylamino)-2,4-pentadienal in various solutions were calculated using RISM-SCF-cSED. The experimental data were well reproduced with an average errors of ∼0.06 eV, using multi-reference perturbation theory.

Analytical energy gradient for the second-order Møller-Plesset perturbation theory coupled with the reference interaction site model self-consistent field explicitly including spatial electron density distribution.

Solvatochromic shifts of the activation free energies are important aspects to consider for reaction control. To predict the energies, the stationary points in a solution must be accurately determined along the reaction pathway. In this study, the second-order Møller-Plesset perturbation (MP2) theory combined with the reference interaction site model was applied using our fitting approach, and the MP2 analytical energy gradient was determined. The coupled-cluster energy and thermal correction were calculated using the MP2 optimized geometry with solvent effect, and the activation free energies of the Diels-Alder reaction between cyclopentadiene and methyl vinyl ketone are within an error of 2 kcal/mol compared with the experimental data.

Nuclear magnetic shielding of molecule in solution based on reference interaction site model self-consistent field with spatial electron density distribution.

A new method for calculating nuclear magnetic shielding in solutions is developed based on the reference interaction site model self-consistent field (RISM-SCF) with spatial electron density distribution (SEDD). In RISM-SCF-SEDD, the electrostatic interaction between the solute and the solvent is described by considering the spread of electron to obtain more realistic electronic structure in solutions. It is thus expected to allow us to predict more quantitative chemical shifts of a wide variety of chemical species in solutions. In this study, the method is applied to a water molecule in water and is validated by examining the dependence of the solvent temperature and density on chemical shifts. The dependence of solvent species is also investigated, and more accurate results are obtained for polar solvents compared to the previous RISM-SCF study. Another application example of this method is the 15N chemical shifts of two azines in water, which is difficult to predict with the polarizable continuum model (PCM). Our results are in good agreement with the previous quantum mechanical/molecular mechanics study and experimental results. It is also shown that our method gives more realistic results for methanol and acetone than the PCM.

Applicability of density functional and wave function theories combined with the three-dimensional reference interaction site model self-consistent field method to the d–d transitions of a transition metal aqua complex

The applicability of density functional theory (DFT) and wave function theory combined with the three-dimensional reference interaction site model self-consistent field method to the d–d transitions of transition metal aqua complexes was examined using [Cr(H2O)6]3+ in aqueous solution as an example. DFTs with hybrid functionals, multiconfigurational self-consistent field followed by perturbation theory, and coupled-cluster singles and doubles (CCSD) followed by the equation of motion CCSD, gave reasonable d–d transition energies.

Effects of Water Addition on a Catalytic Fluorination of Dienamine.

We investigate the effects of water addition on a highly stereocontrolled fluorination of dienamine generated by α-branched enals and 6′-hydroxy-9-amino-9-deoxy-epi-quinidine with N-fluorobenzenesulfonimide (NFSI) in the presence of Brønsted acid both experimentally and theoretically. It is experimentally found that water addition to organic solvent significantly shortens the reaction time whereas excessive water addition decreases the enantiomeric excess. The results calculated with three-dimensional reference interaction site model self-consistent field (3D-RISM-SCF) method are in good agreement with the experimental ones. It is revealed that the shortness of reaction time is caused by the reactant destabilization and that the decrease in enantiomeric excess is due to the difference of hydration free energy between two transition states.

Three-Dimensional Reference Interaction Site Model Self-Consistent Field Study on the Coordination Structure and Excitation Spectra of Cu(II)-Water Complexes in Aqueous Solution.

The molecular and solvation structures of the hydrated Cu2+ ions and their excitation spectra were investigated using the Kohn-Sham density functional theory (DFT) and the three-dimensional reference interaction site model (3D-RISM) self-consistent field method. Five stable geometrical structures were found to exist in aqueous solution: the distorted octahedral [Cu(H2O)6]2+ in C i and D2 h symmetries, the square pyramidal and trigonal bipyramidal [Cu(H2O)5]2+, and the square planar [Cu(H2O)4]2+. The distorted octahedral structure in the C i symmetry is preferred in [Cu(H2O)6]2+, and the square pyramidal and trigonal bipyramidal [Cu(H2O)5]2+ show almost the same stability. Among these geometries, the six-coordinate complex [Cu(H2O)6]2+ in the C i symmetry had the lowest Helmholtz energy. [Cu(H2O)6]2+ had a distorted octahedral structure, that is, two long axial bonds and four short equatorial bonds. The spatial and radial distribution function analyses for [Cu(H2O)5]2+ and [Cu(H2O)4]2+ showed that [Cu(H2O)5]2+ and [Cu(H2O)4]2+ had one and two solvent water molecules that constituted a distorted octahedron with ligand water distribution. The coordination numbers (CNs) derived from the distribution functions were 5.2-5.4 for [Cu(H2O)5]2+ and 5.3 for [Cu(H2O)4]2+. These results indicated that the Cu2+ ion in an aqueous solution had 5-6 coordination water molecules in the first hydration shell and some structures with different CNs may interchange in the solution. The excitation energies and electronic configurations of low-lying d-d excited states were calculated using the time-dependent DFT with the electric field generated by 3D-RISM. The orbital energies and electronic configurations were in a similar picture to those of the classical crystal field theory because of the highly symmetrical features of all structures. In [Cu(H2O)6]2+, the degeneracies of orbitals were resolved, whereas in [Cu(H2O)5]2+ and [Cu(H2O)4]2+, weak and strong quasi-degeneracies remained. As a result, only the four-coordinate complex generated third and fourth excited states, whereas in other complexes, there were no obvious characters of degeneracies. The resulting excitation energies were in good agreement with the absorption spectra.

Dependence of Absorption and Emission Spectra on Polymorphs of Gold(I) Isocyanide Complexes: Theoretical Study with QM/MM Approach

We theoretically investigated phenyl(phenyl isocyanide) gold(I) (PhNC)Au(Ph) 1 and phenyl(dimethylphenyl isocyanide) gold(I) (dimPhNC)Au(Ph) 2 in crystal using our periodic quantum mechanics/molecular mechanics (QM/MM) method based on the self-consistent point charges to elucidate interesting mechano-chemical changes of absorption and emission spectra of 1 and 2 in crystal. To characterize 1 and 2 in crystal, their absorption and emission spectra in crystal were compared to those in gas phase and CHCl3 solvent, where a three-dimensional reference interaction site model self-consistent field (3D-RISM-SCF) was employed to incorporate solvation effect. To investigate the phosphorescence spectrum in crystal, we optimized the geometry of the molecule at the triplet state in crystal which had ground-state geometry because the population of the excited state is generally very small. The QM/MM calculations showed that 1 formed two polymorphs 1b and 1y, 2 formed two polymorphs 2b and 2g, and 1y was more stable tha...

Toward Accurate Solvation Free Energy Calculation with the Reference Interaction Site Model Self-Consistent Field: Introduction of a New Bridge Function.

The reference interaction site model self-consistent field (RISM-SCF) has the potential to become a powerful tool for studying solution chemistry because of its low computational cost and the capability of calculating local solvation structures accurately, such as hydrogen bonding. However, RISM-SCF has a critical weakness: it is not possible to accurately reproduce the experimental data for solvation free energy. In this study, we proposed a new bridge function and combined it with the repulsive bridge correction (RBC) proposed by Kovalenko and Hirata. To verify the effectiveness of our approach, we computed the hydration free energies of 70 organic molecules. Our method successfully improved the overestimation of the cavitation free energy inherent in the original RISM-SCF.