MP2 Results Research Articles

Pharmacophore Oriented MP2 Characterization of Charge Distribution for Anti-SARS-CoV-2 Inhibitor Nirmatrelvir

Quantum mechanical second order Møller–Plesset (MP2) perturbation theory and density functional theory (DFT) Becke, 3-parameter, Lee-Yang-Parr (B3LYP) and Minnesota 2006 local functional (M06L) calculations were performed to optimize structure of nirmatrelvir and compute the Merz-Kollman electrostatic potential (MK ESP), natural population analysis (NPA), Hirshfeld, charge model 5 (CM5), and mulliken partial charges. The mulliken partial charge distribution of nirmatrelvir exhibits a poor correlation with the MK ESP charges in MP2, B3LYP, and M06L calculations respectively. The NPA, Hirshfeld, and CM5 partial charge scheme of nirmatrelvir indicate a reasonable correlation with MK ESP charge assignments in B3LYP and M06L calculations. The above correlations were not improved by the inclusion of implicit solvation model. The MK ESP and CM5 partial charges show a strong correlation between the results of MP2 and two DFT methods. The three optimized structures present a certain degree of differences from the crystal bioactive conformation of nirmatrelvir, suggesting the nirmatrelvir-enzyme complex is formed in the induced-fit model. The Reactivity of warhead electrophilic nitrile is justified by the relatively weaker strength of π bonds in the MP2 calculations. The nirmatrelvir hydrogen bond acceptors consistently show strong delocalization of lone pair electrons in three calculations, whereas hydrogen bond donors are found to have high polarization on the heavy nitrogen atoms in MP2 computations. This work helps to parametrize the force field of nirmatrelvir and improve accuracy of molecular docking and rational inhibitor design.

Structures, binding and clustering energies of [formula omitted] clusters and temperature effects: A DFT study

The study of Cu2+-methanol interactions allows the understanding of metal-alcohol interactions present in many biological and biochemical processes. This work proposes to explore the potential energy of surfaces of the Cu2+(MeOH)n=1-8 clusters in gas phase, temperature-dependence of the relative population, binding and clustering energies of the solvated Cu2+ ion in methanol using M06-2X DFT functional method associated with the 6-31++G** basis set. It emerges new structures are presented for the first time in the literature and the stability rules are respected in almost all sizes. Moreover, the comparison of the length distances of dative bonds obtained with the M06-2X method are in agreement with the experimental results and with the ab initio MP2 method. The M06-2X method is thus presented as an alternative to the MP2 method. The investigation of the temperature dependence of the isomer distribution shows that the most stable and compact structures dominate the population of the studied clusters. For sizes n=2-4, two isomers contribute to the relative population with a dominance of structures in which the methyl group is symmetric, particularly at low temperature. For n⩾6, at least three isomers participate in the population of clusters. Thus, the hexa-, penta- and tera-coordinated structures compete the population of clusters. We also predicted binding and clustering energies as a function of the cluster size, up to n=∞. We propose new values of the electronic binding energy, the binding enthalpy and the free binding energy for the solvation of the Cu2+ ion in methanol. These values are respectively -7150.3, -5974.3 and -4069.5kJ mol−1. Similarly, the values of clustering energies, clustering enthalpy and clustering free energy of Cu2+(MeOH)n clusters, are -113.5, -115.8 and-47.9kJ mol−1 respectively. These energy analyzes are in agreement with the MP2 results and the experimental results obtained in methanol with other dications.

Tetrel Bonding in Anion Recognition: A First Principles Investigation

Twenty-five molecule-anion complex systems [I4Tt···X-] (Tt = C, Si, Ge, Sn and Pb; X = F, Cl, Br, I and At) were examined using density functional theory (ωB97X-D) and ab initio (MP2 and CCSD) methods to demonstrate the ability of the tetrel atoms in molecular entities, I4Tt, to recognize the halide anions when in close proximity. The tetrel bond strength for the [I4C···X-] series and [I4Tt···X-] (Tt = Si, Sn; X = I, At), was weak-to-moderate, whereas that in the remaining 16 complexes was dative tetrel bond type with very large interaction energies and short Tt···X close contact distances. The basis set superposition error corrected interaction energies calculated with the highest-level theory applied, [CCSD(T)/def2-TZVPPD], ranged from -3.0 to -112.2 kcal mol-1. The significant variation in interaction energies was realized as a result of different levels of tetrel bonding environment between the interacting partners at the equilibrium geometries of the complex systems. Although the ωB97X-D computed intermolecular geometries and interaction energies of a majority of the [I4Tt···X-] complexes were close to those predicted by the highest level of theory, the MP2 results were shown to be misleading for some of these systems. To provide insight into the nature of the intermolecular chemical bonding environment in the 25 molecule-anion complexes investigated, we discussed the charge-density-based topological and isosurface features that emanated from the application of the quantum theory of atoms in molecules and independent gradient model approaches, respectively.

Exploring the Limits of Second- and Third-Order Møller-Plesset Perturbation Theories for Noncovalent Interactions: Revisiting MP2.5 and Assessing the Importance of Regularization and Reference Orbitals.

This work systematically assesses the influence of reference orbitals, regularization, and scaling on the performance of second- and third-order Møller-Plesset perturbation theory wave function methods for noncovalent interactions (NCIs). Testing on 19 data sets (A24, DS14, HB15, HSG, S22, X40, HW30, NC15, S66, AlkBind12, CO2Nitrogen16, HB49, Ionic43, TA13, XB18, Bauza30, CT20, XB51, and Orel26rad) covers a wide range of different NCIs including hydrogen bonding, dispersion, and halogen bonding. Inclusion of potential energy surfaces from different hydrogen bonds and dispersion-bound complexes gauges accuracy for nonequilibrium geometries. Fifteen methods are tested. In notation where nonstandard choices of orbitals are denoted as methods:orbitals, these are MP2, κ-MP2, SCS-MP2, OOMP2, κ-OOMP2, MP3, MP2.5, MP3:OOMP2, MP2.5:OOMP2, MP3:κ-OOMP2, MP2.5:κ-OOMP2, κ-MP3:κ-OOMP2, κ-MP2.5:κ-OOMP2, MP3:ωB97X-V, and MP2.5:ωB97X-V. Furthermore, we compare these methods to the ωB97M-V and B3LYP-D3 density functionals, as well as CCSD. We find that the κ-regularization (κ = 1.45 au was used throughout) improves the energetics in almost all data sets for both MP2 (in 17 out of 19 data sets) and OOMP2 (16 out of 19). The improvement is significant (e.g., the root-mean-square deviation (RMSD) for the S66 data set is 0.29 kcal/mol for κ-OOMP2 versus 0.67 kcal/mol for MP2) and for interactions between stable closed-shell molecules, not strongly dependent on the reference orbitals. Scaled MP3 (with a factor of 0.5) using κ-OOMP2 reference orbitals (MP2.5:κ-OOMP2) provides significantly more accurate results for NCIs across all data sets with noniterative O(N6) scaling (S66 data set RMSD: 0.10 kcal/mol). Across the entire data set of 356 points, the improvement over standard MP2.5 is approximately a factor of 2: RMSD for MP3:κ-OOMP2 is 0.25 vs 0.50 kcal/mol for MP2.5. The use of high-quality density functional reference orbitals (ωB97X-V) also significantly improves the results of MP2.5 for NCI over a Hartree-Fock orbital reference. All our assessments and conclusions are based on the use of the medium-sized aug-cc-pVTZ basis to yield results that are directly compared against complete basis set limit reference values.

Exploring the Superhalogen Properties of Polynuclear Structures without Halogen Ligands: A Combined Ab Initio and DFT Study on Triple-Bridged [Mg2L5]-1 (L = -OCN, -SCN) Anions.

Via combined ab initio and DFT calculations, 16 [Mg2(OCN)5]-1 and [Mg2(SCN)5]-1 isomers are studied to explore their potentials as superhalogens. The results of high-level OVGF calculations verify that these systems are superhalogen anions due to their high VDE values which lie within 6.74-7.04 eV and 5.73-6.27 eV for [Mg2(OCN)5]-1 and [Mg2(SCN)5]-1, respectively. The results of low-cost methods, either ab initio or DFT, are generally consistent with those of OVGF, and some of them demonstrate promising accuracy. The best performance of low-cost ab initio methods comes from (HF+MP2)/2, which represents the average value of the MP2 and HF results. In the aspect of DFT, five functionals (CAM-B3LYP, ωB97X-D3, M06, M06-2X, and B2PLYP) provide the most accurate results when compared to OVGF. Thus, these low-cost methods could be used to calculate the VDE value of the future systems of larger size. Useful information about the VDEs of [Mg2(OCN)5]-1 and [Mg2(SCN)5]-1 could be obtained from the analysis of the extra electron density and HOMO as well as spin density.

Applicability of DFT functionals for evaluating the first hyperpolarizability of phenol blue in solution.

The first electronic hyperpolarizability (β) of phenol blue (PB) in several solvents in a wide range of dielectric constants is investigated using the density functional theory (DFT). The reliability of various exchange-correlation functionals is assessed by a comparison to reference Møller-Plesset second-order perturbation theory (MP2) calculations. The equilibrium geometry of PB in each solvent is obtained by using the average solvent electrostatic configuration/free energy gradient method, which performs optimizations on the free energy hyper-surface by employing iteratively the sequential quantum mechanics/molecular mechanics methodology. The dependence of β on the bond length alternation (BLA) coordinate is rationalized by means of the two-level model. Within the employed exchange-correlation functionals, the LC-BLYP functional shows the best performance for describing the static and dynamic MP2 results of β, which increases as the BLA diminishes, reaching a maximum in an intermediate value of BLA. The results also illustrate the role played by the difference between the ground- and excited-state dipole moments (Δμ) in determining the hyperpolarizability behavior in solution. Particularly, in the aqueous solution case, Δμ goes to around zero when BLA is near zero, leading to an abrupt decline in the β value. The DFT results of this study, therefore, indicate a clear relationship between the first hyperpolarizability and the BLA coordinate for the PB in solution, in agreement with experiment.

Benchmarking quantum mechanical methods for calculating reaction energies of reactions catalyzed by enzymes

To assess the accuracy of different quantum mechanical methods for biochemical modeling, the reaction energies of 20 small model reactions (chosen to represent chemical steps catalyzed by commonly studied enzymes) were calculated. The methods tested included several popular Density Functional Theory (DFT) functionals, second-order Møller Plesset perturbation theory (MP2) and its spin-component scaled variant (SCS-MP2), and coupled cluster singles and doubles and perturbative triples (CCSD(T)). Different basis sets were tested. CCSD(T)/aug-cc-pVTZ results for all 20 reactions were used to benchmark the other methods. It was found that MP2 and SCS-MP2 reaction energy calculation results are similar in quality to CCSD(T) (mean absolute error (MAE) of 1.2 and 1.3 kcal mol−1, respectively). MP2 calculations gave a large error in one case, and are more subject to basis set effects, so in general SCS-MP2 calculations are a good choice when CCSD(T) calculations are not feasible. Results with different DFT functionals were of reasonably good quality (MAEs of 2.5–5.1 kcal mol−1), whereas popular semi-empirical methods (AM1, PM3, SCC-DFTB) gave much larger errors (MAEs of 11.6–14.6 kcal mol−1). These results should be useful in guiding methodological choices and assessing the accuracy of QM/MM calculations on enzyme-catalyzed reactions.

Additivity and non-additivity of dissociation energies in intermolecular interactions. Theoretical studies on (H2)n, n = 2-8, (CO2)n, n = 2-6 and (HF)n, n = 2-8

CCSD(T) and MP2 results using the aug-cc-pV5Z basis set are reported for chain, cyclic and other structures of the clusters (H2)n, n = 2-8, (CO2)n, n = 2-6 and (HF)n, n = 2-8. In chain-like structures of (H2)n and (CO2)n, with the bonding type of the dimer maintained, the dissociation energy De of the dimer doubles for the trimer, triples for the tetramer, and so on. Due to these systems being dominated by short-range forces, interactions are essentially restricted to neighbouring monomers. For other types of (H2)n and (CO2)n structures, the multipliers relative to the dimerisation energy can be much higher. Dissociation energies for the hexamers in S6 symmetry of both H2 (379 cm−1) and CO2 (4925 cm−1) are over ten times the respective dimerisation energies. For the chain-like trimer of HF, however, De is in excess of double the dimer value. Mainly due to longer-range dipolar forces, the interactions reach beyond the neighbouring monomers. The interaction energy between HF monomers in chains follows an approximate R−2 (R being the F–F distance) relationship, The calculated dissociation energies of the HF octamer are 15,985 cm−1 (factor of 10.4) for the chain, and 21,003 cm−1 (factor of 13.7) for the C6h cyclic structure.

Investigating the spin state and electronic structure of the Fe3O cluster from MOF MIL-100(Fe)

In this paper, we investigate the spin state of the Fe3O cluster from MIL-100(Fe), each Fe site of which possesses either one unpaired electron, three unpaired electrons, or five unpaired electrons. Total energies with respect to different spin states were optimized with the PBE, B3LYP, HF, and MP2 methods in combination with various basis sets (6-31G, 6-31G*, 6-311G(d,p)) for non-metal ions and pseudopotentials for Fe (SDD and LanL2DZ). The results of B3LYP, MP2, and HF methods predicted that each Fe site had five unpaired electrons in the most stable spin state. However, the results of PBE show two opposite cases. In one case, PBE predicted each Fe had one unpaired electron, while in the remaining PBE cases, each Fe site was predicted to exhibit five unpaired electrons. We finally conclude the Fe3O cluster with 15 unpaired electrons is the most stable structure.

A Quadratic Pair Atomic Resolution of the Identity Based SOS-AO-MP2 Algorithm Using Slater Type Orbitals

We report a production level implementation of pair atomic resolution of the identity (PARI) based second-order Møller–Plesset perturbation theory (MP2) in the Slater type orbital (STO) based Amsterdam Density Functional (ADF) code. As demonstrated by systematic benchmarks, dimerization and isomerization energies obtained with our code using STO basis sets of triple-ζ-quality show mean absolute deviations from Gaussian type orbital, canonical, basis set limit extrapolated, global density fitting (DF)-MP2 results of less than 1 kcal/mol. Furthermore, we introduce a quadratic scaling atomic orbital based spin-opposite-scaled (SOS)-MP2 approach with a very small prefactor. Due to a worst-case scaling of , our implementation is very fast already for small systems and shows an exceptionally early crossover to canonical SOS-PARI-MP2. We report computational wall time results for linear as well as for realistic three-dimensional molecules and show that triple-ζ quality calculations on molecules of several hundreds of atoms are only a matter of a few hours on a single compute node, the bottleneck of the computations being the SCF rather than the post-SCF energy correction.

Microsolvation Structures of Protonated Glycine and l-Alanine.

The IR predissociation spectra of microsolvated glycine and l-alanine, GlyH+(H2O) n and AlaH+(H2O) n, n = 1-6, are presented. The assignments of the solvation structures are aided by H2O/D2O substitution, IR-IR double resonance spectroscopy, and computational efforts. The analysis reveals the water-amino acid as well as the water-water interactions, and the subtle effects of the methyl side chain in l-alanine on the solvation motif are also highlighted. The bare amino acids exhibit an intramolecular hydrogen bond between the protonated amine and carboxyl terminals. In the n = 1-2 clusters, the water molecules preferentially solvate the protonated amine group, and we observed differences in the relative isomer stabilities in the two amino acids due to electron donation from the methyl weakening the intramolecular hydrogen bond. The structures in the n = 3 clusters show a further preference for solvation of the carboxyl group in l-alanine. For n = 4-6 clusters, the solvation structure of the two amino acids is remarkably similar, with one dominant isomer present in each cluster size. The first solvation shell is completed at n = 4, evidenced by a lack of free NH and OH stretches on the amino acid, as well as the first observation of H2O-H2O interactions in the spectra of n = 5. Finally, we note that calculations at the density functional theory (DFT) level show excellent agreement with the experiment for the smaller clusters. However, when water-water interactions compete with water-amino acid interactions in the larger clusters, DFT results show greater disagreement with experiment when compared to MP2 results.

Hydrogen Activation by Silica-Supported Metal Ion Catalysts: Catalytic Properties of Metals and Performance of DFT Functionals.

Single-site heterogeneous catalysts (SSHC) have received increasing attention due to their well-defined active sites and potentially high specific activity. Detailed computational studies were carried out on a set of potential SSHC's, i.e., silica-supported metal ions, to investigate the reactivity of these catalysts with H2 as well as to evaluate the performance of density functional theory (DFT) methods in conjunction with triple-ζ quality basis sets (i.e., cc-pVTZ) on reaction energetics. The ions considered include 4d and 5d metals as well as several post-transition metal ions. A representative cluster model of silica is used to calculate reaction free energies of the metal hydride formation that results from the heterolytic cleavage of H2 on the M-O bond. The hydride formation free energy is previously shown to be strongly correlated with the catalytic activity of such catalysts for alkene hydrogenation. ONIOM calculations (CCSD(T)//MP2) are used to assess the accuracy and reliability of the MP2 results and it is found that MP2 is a suitable level of theory for gauging the performance of DFT functionals. The performance of various DFT functionals is assessed relative to MP2 results and it is found that the wB97xd and PBE0 functionals have the lowest standard deviation (STD) value while the MN12SX and PBE functionals have the lowest mean absolute deviation (MAD) values. The B3LYP functional is shown to have similar MAD and STD values as the top performing functionals. Potential active SSHC's for exergonic hydrogen activation predicted in this study include mostly late and post transition metal ions, i.e., Au3+, Pd2+, Pt4+, Pd4+, Ir4+, Hg2+, Rh3+, Pb4+, Tl3+, In3+, Ir3+, Os4+, Cd2+, Ru2+, and Ga3+. This study provides important guidance to future computational studies of such catalyst systems.

Superalkali Cations with Trivalent Anion MF63− (M = Al, Ga, Sc) as Central Core

A new series of polynuclear cations MF6Li4+ (M = Al, Ga, Sc) have been theoretically investigated based on density functional theory calculations. The regular octahedral MF6 groups, although maintained their integrity, distorted to some degree upon the introduction of Li ligands. It has been found that the Li ligands prefer to occupy the bridge- or hollow-site of the MF6 core. According to the MP2 results, the MF6Li4+ cations have lower vertical electron affinities (EAvert, 2.618–3.212 eV) than the threshold of 3.89 eV, verifying their superalkali identity. Besides, the MF6Li4+ configurations with more dispersive Li ligands possess lower EAvert values. More importantly, large HOMO–LUMO gaps, binding energies per atom (Eb), and positive fragmentation energies ensure the stability of these cations.

Proposed Hydrogen-Bonding Index of Donor or Acceptor Reflecting Its Intrinsic Contribution to Hydrogen-Bonding Strength.

In this work, we tentatively propose that the hydrogen-bonding strength EHB (referring to the minimal hydrogen-bonding energy) and its corresponding hydrogen-bond (HB) distance (referring to the optimal HB distance dHB) for simple mono-HB systems have an exponential relationship on the basis of MP2 and DFT computational results. We take a step further and propose that the hydrogen-bonding indices of the donor (Idonor) and acceptor (Iacceptor), reflecting their intrinsic contributions to hydrogen-bonding strength, also have an exponential relation with the hypothetical effective hydrogen-bond radii of the donor (rdonor) and acceptor (racceptor), respectively. On the basis of extensive quantum-mechanical calculations, relevant assumptions about the hydrogen-bonding index are rationalized. Moreover, the hydrogen-bonding index is also suggested as an additional prefiltering criterion for virtual screening besides the widely accepted Lipinski's rule of five. Finally, a "Hydrogen-Bond Index Estimator (HBIE)" module has been implemented in our Visual Force Field Derivation Toolkit (VFFDT) program to approximately and rapidly estimate the hydrogen-bonding indices of any small molecules in batch and screen possible stronger donors or acceptors from the small-molecule database. To the best of our knowledge, the concept of the hydrogen-bonding index and its potential application are proposed here for the first time.

The microwave spectrum of ferrocenecarboxylic acid

The microwave spectrum was measured for ferrocenecarboxylic acid in the 4.8–9.8GHz range using a pulsed-beam Fourier transform microwave spectrometer. 27 transitions were measured and assigned, which include a-, b-, and c-type rotational transitions. From the measured transitions, the rotational and centrifugal distortion constants were determined. The values determined are A=1138.0162(13)MHz, B=653.81796(54)MHz, C=559.83162(47)MHz, DJ = 0.0675(52)kHz, DJK=−0.157(36)kHz, DK=0.193(47)kHz, and dJ = 0.0194(22)kHz. MP2 and B3LYP gas phase structure optimizations were performed with the aug-cc-pVTZ basis and the B3LYP method yielded rotational constants that were in far better agreement with the experimentally determined values than the MP2 results.

Conventional and Explicitly Correlated ab Initio Benchmark Study on Water Clusters: Revision of the BEGDB and WATER27 Data Sets.

Benchmark ab initio energies for BEGDB and WATER27 data sets have been re-examined at the MP2 and CCSD(T) levels with both conventional and explicitly correlated (F12) approaches. The basis set convergence of both conventional and explicitly correlated methods has been investigated in detail, both with and without counterpoise corrections. For the MP2 and CCSD-MP2 contributions, rapid basis set convergence observed with explicitly correlated methods is compared to conventional methods. However, conventional, orbital-based calculations are preferred for the calculation of the (T) term, since it does not benefit from F12. CCSD(F12*) converges somewhat faster with the basis set than CCSD-F12b for the CCSD-MP2 term. The performance of various DFT methods is also evaluated for the BEGDB data set, and results show that Head-Gordon's ωB97X-V and ωB97M-V functionals outperform all other DFT functionals. Counterpoise-corrected DSD-PBEP86 and raw DSD-PBEPBE-NL also perform well and are close to MP2 results. In the WATER27 data set, the anionic (deprotonated) water clusters exhibit unacceptably slow basis set convergence with the regular cc-pVnZ-F12 basis sets, which have only diffuse s and p functions. To overcome this, we have constructed modified basis sets, denoted aug-cc-pVnZ-F12 or aVnZ-F12, which have been augmented with diffuse functions on the higher angular momenta. The calculated final dissociation energies of BEGDB and WATER27 data sets are available in the Supporting Information. Our best calculated dissociation energies can be reproduced through n-body expansion, provided one pushes to the basis set and electron correlation limit for the two-body term; for the three-body term, post-MP2 contributions (particularly CCSD-MP2) are important for capturing the three-body dispersion effects. Terms beyond four-body can be adequately captured at the MP2-F12 level.

Capturing Many-Body Interactions with Classical Dipole Induction Models.

The nonadditive many-body interactions are significant for structural and thermodynamic properties of condensed phase systems. In this work we examined the many-body interaction energy of a large number of common organic/biochemical molecular clusters, which consist of 18 chemical species and cover nine common organic elements, using the Møller–Plesset perturbation theory to the second order (MP2) [Møller et al. Phys. Rev.1934, 46, 618.]. We evaluated the capability of Thole-based dipole induction models to capture the many-body interaction energy. Three models were compared: the original model and parameters used by the AMOEBA force field, a variation of this original model where the damping parameters have been reoptimized to MP2 data, and a third model where the damping function form applied to the permanent electric field is modified. Overall, we find the simple classical atomic dipole models are able to capture the 3- and 4-body interaction energy across a wide variety of organic molecules in various intermolecular configurations. With modified Thole models, it is possible to further improve the agreement with MP2 results. These models were also tested on systems containing metal/halogen ions to examine the accuracy and transferability. This work suggests that the form of damping function applied to the permanent electrostatic field strongly affects the distance dependence of polarization energy at short intermolecular separations.

Prediction of the rotational spectra of microsolvated complexes with low cost DFT methods

Some of the most used DFT methods together with MP2 have been tested using 6-311++G(d,p) and TZVP basis sets to probe their usefulness in prediction of the rotational spectra of several microsolvated complexes of formamide, t-N-methylformamide, glycine and β-propiolactone. Results obtained for the rotational parameters and the prediction of the spectra have been compared to experimental data previously measured by Fourier Transform Microwave Spectroscopy. Analysis of the standard deviation of the predicted rotational spectra for all the levels tested indicates that the methods which better approach to the MP2 results are mPW91LYP and B3LYP-D3.

Cu(H2O) n ]2+ (n = 1–6) complexes in solution phase: a DFT hierarchical study

For the theoretical modeling of energy profiles of Cu2+ reactions with biological ligands, it is indispensable to know the structure of its solvation sphere. Not withstanding the experimental and theoretical studies on this topic, nature of Cu–water complexes is still subject of intense debate. In order to gain insight into the structural features and relative stabilities of the [Cu(H2O) n ]2+ (n = 1–6) species, several of their coordination modes considering water molecules in the first and second hydration shell of Cu2+, have been considered. Electronic structure calculations were performed with the G09 quantum chemistry suite of programs. Geometries are optimized by means of DFT functionals (allocate in different rungs of the Jacob’s ladder) and the ab initio MP2 perturbation theory applying the def-SVP valence split basis set; formation of complexes is studied in gas phase and solution by application of CPCM and SMD protocols. Stabilization energies for each stoichiometry are calculated at the MP2/aug-cc-pVTZ level of theory. [Cu(H2O)2]2+, [Cu(H2O)3]2+ and [Cu(H2O)4]2+ complexes show lineal, planar trigonal and square planar structures, respectively; gas phase and CPCM results indicate that [Cu(H2O)5]2+ is isoenergetic with [Cu(H2O)4]2+(H2O), but SMD solvent effects favor formation of intramolecular hydrogen bonds. For sixfold complexes, [Cu(H2O)4]2+(H2O)2 is consistently found to be the most stable compared with [Cu(H2O)6]2+ and [Cu(H2O)5]2+(H2O). For n = 5 and 6, hydrogen bond formation in the second hydration shell competes with coordination in axial positions; results indicate that this intramolecular hydrogen bond stabilizes the complex more than axial coordination of water. In gas phase as well as solution, BHLYP outcomes are always consistent with MP2 results, evidencing the importance of exact exchange in the functional. SMD solvent effects show that water ligands are more loosely bond to the central ion that might explain a variety of complexes coexisting in solution, contrasting with gas phase where releasing a water molecule entails a higher energetic cost. Results indicate a clear tendency to improve the geometry, the symmetry and the relative stabilization energy of the Cu–water complex, toward the MP2 value, when either advancing on the Jacob’s ladder or the percentage of exact exchange in the functional increases.

Assessment of the performance of commonly used DFT functionals vs. MP2 in the study of IL-Water, IL-Ethanol and IL-(H2O)3 clusters

We present a comparative study of the accuracy of different DFT approaches vs. MP2 for evaluating ionic liquids (ILs)+cosolvent. Namely, we are interested in [XBmim]+cosolvent (X being Cl−, BF4−, PF6−, and CH3SO3− anions and cosolvent being water or ethanol) and [XBmim]+(H2O)3 clusters. In this study the B3LYP, B3LYP-D3, M06, M06-2X and M06-HF functionals with Pople and Dunning basis sets are considered. We find that the influence of the basis sets is a factor to take into consideration. As already seen for weakly bonded systems when the basis set quality is low the uncorrected counterpoise (unCP) or averaging counterpoise (averCP) energies must be used due to cancellation errors. Besides, the inclusion of extra diffuse functions and polarization is also required specially in the case of ILs interacting with water clusters. The B3LYP functional does not reproduce either the structure or the interaction energies for ILs+H2O and ILs+EtOH aggregates, the energetic discrepancies being more significant than the structural ones. Among the dispersive corrected functionals, M06-2X results resemble to a great extent the reference data when the unCP interaction energies are considered for both water and ethanol. In turn, M06 and B3LYP-D3 functionals are the best option for ILs containing polar and non-polar anions, respectively, whether the averCP interactions energies are taking into consideration. From the structural point of view, B3LYP and M06 functionals describe more open structures whereas B3LYP-D3, M06-2X and M06-HF structures resemble quite well MP2 results. When the number of water molecules increases the H bonding motif gains importance and the effect depends on the underlying functional. Only M06-2X and M06-HF behaviour is similar to that observed for one water molecule. This is important because to describe ILs-cosolvent solutions is not only necessary to take into account the ILs-cosolvent interactions but also the cosolvent-cosolvent ones in the ensemble of the system.