Estimating relative free energies from a single ensemble: Hydration free energies

The ability to determine the free energy of solvation for a number of small organic molecules with varying sizes and properties from the coordinate trajectory of a single simulation of a given reference state was investigated. The relative free energies were estimated from a single step perturbation using the perturbation formula. The reference state consisted of a cavity surrounded by solvent. To enhance sampling a soft-core interaction was used for the cavity. The effect of the size of the cavity, the effective core height, and the length of simulation on the ability to reproduce results obtained from thermodynamic integration calculations was considered. The results using a single step perturbation from an appropriately chosen initial state were comparable to results from thermodynamic integration calculations for a wide range of compounds. Using a large number of compounds the computational efficiency was potentially increased by 2–3 orders of magnitude over traditional free energy approaches. Factors determining the efficiency of the approach are discussed. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1604–1617, 1999     

Influence of a Pre-organized N-Donor Group on the Coordination of Trivalent Actinides and Lanthanides by an Aminopolycarboxylate Complexant

The thermodynamic influence of a pre-organized N-donor group on the coordination of trivalent actinides and lanthanides by an aqueous aminopolycarboxylate complexant has been investigated. The synthesized reagent, N-2-methylpicolinate-ethylenediamine-N,N′,N′-triacetic acid (EDTA-Mpic), resembles ethylenediamine-N,N,N′,N′-tetraacetic acid (EDTA) with a single acetate pendant arm replaced by a 6-carboxypyridin-2-ylmethyl group. The rigid N-donor picolinate functionality has a profound impact on ligand protonation and trivalent f element complexation equilibria, as demonstrated by potentiometric, spectroscopic, and liquid/liquid metal-partitioning studies as well as by molecular dynamics calculations. Relative to diethylenetriamine-N,N,N′,N′′,N′′-pentaacetic acid (DTPA), the ability to preferentially bind trivalent actinides over trivalent lanthanides was moderately lowered due to the presence of the N-(6-carboxypyridin-2-ylmethyl) substituent. The structural modification substantially amplifies the total ligand acidity of EDTA-Mpic. As a result the complexant sustains the metal complexation and efficient An³⁺/Ln³⁺ differentiation in aqueous mixtures of unprecedented acidity for this class of reagents.     

A Systemic Insight into Exohedral Actinides and Endohedral Borospherenes: An&Bm and An@Bn (An=U,Np, Pu; m = 28, 32, 34, 36, 38, 40; n = 36, 38, 40)

A series of exohedral actinide borospherenes, An&B_m, and endohedral borospherenes, An@B_n (An=U, Np, Pu; m = 28, 32, 34, 36, 38, 40; n = 36, 38, 40), have been characterized by density functional theory calculations. The electronic structures, chemical bond topological properties and spectra have been systematically investigated. It was found that An@B_n is more stable than An&B_n in terms of structure and energy, and UB₃₆ in an aqueous solution is the most stable molecular in this research. The IR and UV-vis spectra of An&B_m and An@B_n are computationally predicted to facilitate further experimental investigations. Charge-transfer spectroscopy decomposes the total UV-Vis absorption curve into the contributions of different excitation features, allowing insight into what form of electronic excitation the UV–Vis absorption peak is from the perspective of charge transfer between the An atoms and borospherenes.     

Assessing the Accuracy of SAPT(DFT) Interaction Energies by Comparison with Experimentally Derived Noble Gas Potentials and Molecular Crystal Lattice Energies

The density functional version of symmetry‐adapted perturbation theory, SAPT(DFT), is a computationally efficient method for calculating intermolecular interaction energies. We evaluate its accuracy by comparison with experimentally determined noble gas interaction potentials and sublimation enthalpies, most of which have not been previously calculated using this method. In order to compare the results with wavefunction methods, we also calculate these quantities using MP2 and, for noble gas dimers, using CCSD(T). For the crystal lattice energy calculations, we include corrections to the dispersion, electrostatic, and induction energies that account for the finite interaction distance cutoff and higher‐order induction contributions. Overall, the energy values extrapolated to the complete basis set limit show that SAPT(DFT) achieves significantly better agreement with experiment than MP2.     

Large-Sized Ammonia Clusters and Solvation Energies of the Proton in Ammonia

The absolute solvation energies (free energies and enthalpies) of the proton in ammonia are used to compute the pK_a of species embedded in ammonia. They are also used to compute the solvation energies of other ions in ammonia. Despite their importance, it is not possible to determine experimentally the solvation energies of the proton in a given solvent. We propose in this work a direct approach to compute the solvation energies of the proton in ammonia from large-sized neutral and protonated ammonia clusters. To undertake this investigation, we performed a geometry optimization of neutral and protonated ammonia 30-mer, 40-mer, and 50 mer to locate stable structures. These structures have been fully optimized at both APFD/6-31++g(d,p) and M06-2X/6-31++g(d,p) levels of theory. An infrared spectroscopic study of these structures has been provided to assess the reliability of our investigation. Using these structures, we have computed the absolute solvation free energy and the absolute solvation enthalpy of the proton in ammonia. It comes out that the absolute solvation free energy of the proton in ammonia is calculated to be −1192 kJ mol^–1, whereas the absolute solvation enthalpy is evaluated to be −1214 kJ mol^–1. © 2019 Wiley Periodicals, Inc.     

On the nature of DNA-duplex stability

The unwinding free energy of 128 DNA octamers was correlated with the sum of interaction energies among DNA bases and their solvation energies. The former energies were determined by using the recently developed density functional theory procedure augmented by London dispersion energy (RI-DFT-D) that provides accurate hydrogen-bonding and stacking energies highly comparable with CCSD(T)/complete basis set limit benchmark data. Efficient tight-binding DFT covering dispersion energy was also used and yielded satisfactory results. The latter method can be used for extended systems. The solvation energy was determined by using a C-PCM continuum solvent at HF level calculations. Various models were adopted to correlate theoretical energies with experimental unwinding free energies. Unless all energy components (hydrogen-bonding, intra- and interstrand-stacking, and solvation energies) were included and weighted individually, no satisfactory correlation resulted. The most advanced model yielded very close correlation (RMSE=0.32 kcal mol(-1)) fully comparable with the entirely empirical correlation introduced in the original paper. Analysis of the theoretical results shows the importance of inter- and intramolecular stacking energies, and especially the latter term plays a key role in determining DNA-duplex stabilization.     

基于分子动力学模拟和连续介质模型的自由能计算方法*

近些年,基于分子动力学模拟和连续介质模型的自由能计算方法受到了越来越多的关注,其中MM/PBSA就是最具代表性的方法.在MM/PBSA中,体系的焓变采用分子力学(MM)的方法计算得到;溶剂效应中极性部分对自由能的贡献通过解Poisson-Boltzmann(PB)方程的方法计算得到;溶液效应中非极性部分对自由能的贡献则通过分子表面积(SA)计算得到.本文结合我们科研组的工作,就近几年MM/PBSA方法的最新进展做了较为详细的阐述,同时对MM/PBSA的发展前景进行了展望.     

A theoretical study of the structure and bonding of UOX4 (X = F, Cl, Br, I) molecules: the importance of inverse trans influence.

During nitroxide-mediated polymerization (NMP) in the presence of a nitroxide R2(R1)NO*, the reversible formation of N-alkoxyamines [P-ON(R1)R2] reduces significantly the concentration of polymer radicals (P*) and their involvement in termination reactions. The control of the livingness and polydispersity of the resulting polymer depends strongly on the magnitude of the bond dissociation energy (BDE) of the C-ON(R1)R2 bond. In this study, theoretical BDEs of a large series of model N-alkoxyamines are calculated with the PM3 method. In order to provide a predictive tool, correlations between the calculated BDEs and the cleavage temperature (T(c)), and the dissociation rate constant (k(d)), of the N-alkoxyamines are established. The homolytic cleavage of the N-OC bond is also investigated at the B3P86/6-311++G(d,p)//B3LYP/6-31G(d), level. Furthermore, a natural bond orbital analysis is carried out for some N-alkoxyamines with a O-C-ON(R1)R2 fragment, and the strengthening of their C-ON(R1)R2 bond is interpreted in terms of stabilizing anomeric interactions.     

Accurate pKa determination for a heterogeneous group of organic molecules.

Single-molecule studies that allow to compute pKa values, proton affinities (gas-phase acidity/basicity) and the electrostatic energy of solvation have been performed for a heterogeneous set of 26 organic compounds. Quantum mechanical density functional theory (DFT) using the Becke-half&half and B3LYP functionals on optimized molecular geometries have been carried out to investigate the energetics of gas-phase protonation. The electrostatic contribution to the solvation energies of protonated and deprotonated compounds were calculated by solving the Poisson equation using atomic charges generated by fitting the electrostatic potential derived from the molecular wave functions in vacuum. The combination of gas-phase and electrostatic solvation energies by means of the thermodynamic cycle enabled us to compute pKa values for the 26 compounds, which cover six distinct chemical groups (carboxylic acids, benzoic acids, phenols, imides, pyridines and imidazoles). The computational procedure for determining pKa values is accurate and transferable with a root-mean-square deviation of 0.53 and 0.57 pKa units and a maximum error of 1.0 pKa and 1.3 pKa units for Becke-half&half and B3LYP DFT functionals, respectively.     

Solvation effects on reaction profiles by the polarizable continuum model coupled with the Gaussian density functional method

An efficient version of the polarizable continuum model for solvation has been implemented in the Gaussian density-functional-based code called deMon. Solvation free energies of representative compounds have been calculated as a preliminary test. The hydration effects on the reaction profile of the Cl⁻+CH₃Cl→ClCH₃+Cl⁻ reaction and the thermodynamics of the Menschutkin reaction have also been investigated. Finally, the conformational behavior of the 1,2-diazene cis–trans isomerization process in water was examined. Comparisons between the results obtained and the available experimental data and previous theoretical computations have been made. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 290–299, 1998     

On the nature of actinide- and lanthanide-metal bonds in heterobimetallic compounds

Eleven experimentally characterized complexes containing heterobimetallic bonds between elements of the f-block and other elements were examined by quantum chemical methods: [(η(5)-C(5)H(5))(2)(THF)LuRu(η(5)-C(5)H(5))(CO)(2)], [(η(5)-C(5)Me(5))(2)(I)ThRu(η(5)-C(5)H(5))(CO)(2)], [(η(5)-C(5)H(5))(2)YRe(η(5)-C(5)H(5))(2)], [{N(CH(2)CH(2)NSiMe(3))(3)}URe(η(5)-C(5)H(5))(2)], [Y{Ga(NArCh)(2)}{C(PPh(2)NSiH(3))(2)}(CH(3)OCH(3))(2)], [{N(CH(2)CH(2)NSiMe(3))(3)}U{Ga(NArCH)(2)}(THF)], [(η(5)-C(5)H(5))(3)UGa(η(5)-C(5)Me(5))], [Yb(η(5)-C(5)H(5)){Si(SiMe(3))(3)(THF)(2)}], [(η(5)-C(5)H(5))(3)U(SnPh(3))], [(η(5)-C(5)H(5))(3)U(SiPh(3))], and (Ph[Me]N)(3)USi(SiMe(3))(3). Geometries in good agreement with experiment were obtained at the density functional level of theory. The multiconfigurational complete active space self-consistent field method (CASSCF) and subsequent corrections with second order perturbation theory (CASPT2) were applied to further understand the electronic structure of the lanthanide/actinide-metal (or metal-metalloid) bonds. Fragment calculations and energy-decomposition analyses were also performed and indicate that charge transfer occurs from one supported metal fragment to the other, while the bonding itself is always dominated by ionic character.     

Dramatic Increase in the Oxygen Reduction Reaction for Platinum Cathodes from Tuning the Solvent Dielectric Constant

Hydrogen fuel cells (FC) are considered essential for a sustainable economy based on carbon‐free energy sources, but a major impediment are the costs. First‐principles quantum mechanics (density functional theory including solvation) is used to predict how the energies and barriers for the mechanistic steps of the oxygen reduction reaction (ORR) over the fcc(111) platinum surface depend on the dielectric constant of the solvent. The ORR kinetics can be strongly accelerated by decreasing the effective medium polarizability from the high value it has in water. Possible ways to realize this experimentally are suggested. The calculated volcano structure for the dependence of rate on solvent polarization is considered to be general, and should be observed in other electrochemical systems.     

Performance of TDDFT Vertical Excitation Energies of Core-Substituted Naphthalene Diimides

We have evaluated the performance of various density functionals, covering generalized gradient approximation (GGA), global hybrid (GH) and range-separated hybrid (RSH), using time dependent density functional theory (TDDFT) for computing vertical excitation energies against experimental absorption maximum (λ_max) for a set of 10 different core-substituted naphthalene diimides (cNDI) recorded in dichloromethane. The computed excitation in case of GH PBE0 is most accurate while the trend is most systematic with RSH LCY-BLYP compared to λ_max. We highlight the importance of including solvent effects for optimal agreement with the λ_max. Increasing the basis set size from TZ2P to QZ4P has a negligible influence on the computed excitation energies. Notably, RSH CAMY-B3LYP gave the least error for charge-transfer excitation. The poorest agreement with λ_max is obtained with semi-local GGA functionals. Use of the optimally-tuned RSH LCY-BLYP* is not recommended because of the high computational cost and marginal improvement in results.     

A Molecular Theory of the Hydration Force in an Electrolyte Solution

A model, consisting of a pair of large macroions in a dipolar hard sphere-point ion electrolyte, is considered in order to evaluate the hydration force (solvent-mediated) contribution to the force between colloidal particles, which is missing in the DLVO theory. Using the mean spherical approximation (MSA), an explicit expression for this force is obtained. It is shown that the force consists of the hard-core exclusion term that was proposed recently by Henderson and Lozada-Cassou (HLC) [J. Colloid Interface Sci.121, 486 (1988)], and a dipole alignment contribution that originates from the orientational ordering of the solvent molecules near the colloidal particles. The long-range asymptotic form of the total force is given by a Coulomb contribution and is described by the Poisson–Boltzmann or Derjaguin–Landau–Verwey–Overbeek (DLVO) result. The hydration force is short-ranged and extends about ten solvent layers and is responsible for the oscillations of the total force. The total force that we obtain is similar to the semiempirical result of HLC. The comparison with the experimental results for a 10⁻³M KCl electrolyte solution is discussed.     

Magnetic Properties and Electronic Structure of Neptunyl(VI) Complexes: Wavefunctions,Orbitals, and Crystal‐Field Models

The electronic structure and magnetic properties of neptunyl(VI), NpO₂²⁺, and two neptunyl complexes, [NpO₂(NO₃)₃]^? and [NpO₂Cl₄]^2?, were studied with a combination of theoretical methods: ab initio relativistic wavefunction methods and density functional theory (DFT), as well as crystal‐field (CF) models with parameters extracted from the ab initio calculations. Natural orbitals for electron density and spin magnetization from wavefunctions including spin–orbit coupling were employed to analyze the connection between the electronic structure and magnetic properties, and to link the results from CF models to the ab initio data. Free complex ions and systems embedded in a crystal environment were studied. Of prime interest were the electron paramagnetic resonance g‐factors and their relation to the complex geometry, ligand coordination, and nature of the nonbonding 5f orbitals. The g‐factors were calculated for the ground and excited states. For [NpO₂Cl₄]^2?, a strong influence of the environment of the complex on its magnetic behavior was demonstrated. Kohn–Sham DFT with standard functionals can produce reasonable g‐factors as long as the calculation converges to a solution resembling the electronic state of interest. However, this is not always straightforward.