Ni, Cu, Zn, Pd, Ag and Cd Tetraphenylporphyrin Ab Initio Thermochemistry: Enthalpy of Formation of ZnTPP Revisited.

Groups 10-12 metalloporphyrins have been recognized for their numerous properties essential for the development of new sensing materials. In this work, accurate gas-phase enthalpies of formation, ΔfHm0(g,298.15), are predicted for the series of Ni, Cu, Zn, Pd, Ag, and Cd tetraphenylporphyrins (MTPPs) on the basis of the reaction-based Feller-Peterson-Dixon approach and high-level ab initio DLPNO-CCSD(T) calculations. Our recently developed automatic generator of the balanced chemical reactions was employed to reduce the bias of the theoretical ΔfHm0(g,298.15) toward a particular reaction. Theoretical ΔfHm0(g,298.15) for ZnTPP (227.0 ± 3.4 kcal mol-1) does not support the previously reported experimental value of 132 ± 2 kcal mol-1. The origin of the discrepancy probably lies in the experimental solid-state ΔfHm0(ZnTPP, cr,298.15) as it stems from our theoretical evaluations of the ΔfHm0(cr,298.15) values for the entire set of transition metal TPP complexes. The large discrepancy between experiment and theory also holds when different DFT functionals (ωB97M-V, PBE0-D4, and B3LYP-D4) paired with quadruple-ζ quality basis sets are used for the theoretical calculations. Experimental revisiting of the solid-state enthalpy of formation of ZnTPP and analogue measurements for other transition metal TPPs are needed to resolve the observed discrepancy. Based on the predicted enthalpies of formation of MTPPs, the relative energies of the metal-ligand bonding are evaluated and the trends are compared to those for the complexes of the unsubstituted porphyrin with the same set of metals derived in [Can. J. Chem., 2009, 87, 1063]. According to both studies, Pd complexes exhibit the strongest bonding, while the Cd species are the least stable metallocomplexes within the considered series.

Measurement of gravitational and thermal effects in a liquid-actuated torsion pendulum.

We describe a proof-of-principle experiment aiming to investigate the inverse-square law of gravitation at the centimeter scale. The sensor is a two-stage torsion pendulum, while actuation is accomplished by a variable liquid mass. The time-varying gravitational force is related to the level of the circulating fluid in one or two containers at a short distance from the test mass, with all moving mechanical parts positioned at a large distance. We provide a description of the apparatus and present the first results. We identified a systematic effect of thermal origin, producing offsets of few fNm in torque and of about 10 pN in force. When this effect is neutralized, the measurements agree well with the predictions of simulations. We also discuss the upcoming instrument upgradations and the expected sensitivity improvement that will allow us to perform measurements with adequate accuracy to investigate the unexplored regions of the α-λ parameter space of a Yukawa-like deviation from the Newtonian potential.

Solv: An Alternative Continuum Model Implementation Based on Fixed Atomic Charges, Scaled Particle Theory, and the Atom-Atom Potential Method.

An alternative continuum model implementation is reported. The electrostatic contribution to the solvation Gibbs free energy utilizes the noniterative conductor-like screening model of Vyboishchikov and Voityuk (DOI: 10.1002/jcc.26531) based on the fixed partial atomic charges. The nonelectrostatic solute-solvent dispersion-repulsion energy is calculated through the Caillet-Claverie atom-atom potential method employing the grid-based approach. The nonelectrostatic cavitation energy is computed within the scaled particle theory (SPT) formalism with the solute hard-sphere radius obtained via the Pierotti-Claverie (PC) scheme, from the solute molecular surface (SPT-S) or volume (SPT-V). The solvent hard-sphere radius is derived through the fitting to the experimental total solvation free energies of 2530 neutral species in 92 solvents. Application of the model to reproduce both the absolute and relative (reaction net) solvation free energies indicates that the SPT-V approach based on the CM5 charges is the best performer. The method is suggested for the solvation free energy calculation in the nonaqueous solvents.

Gas-phase thermochemistry of noncovalent ligand-alkali metal ion clusters: An impact of low frequencies.

The experimental gas-phase thermochemistry of reactions: M+ (S)n-1 + S → M+ (S)n and M+ + nS→ M+ (S)n , where M is an alkali metal and S is acetonitrile/ammonia, is reproduced. Three approximations are tested: (1) scaled rigid-rotor-harmonic-oscillator (sRRHO); (2) the sRRHO(100) identical to (1), but with all vibrational frequencies smaller than 100 cm-1 replaced with 100 cm-1 ; (3) Grimme's modified scaled RRHO (msRRHO) (Grimme, Chem. Eur. J., 2012, 18, 9955-9964). The msRRHO approach provides the most accurate reaction entropies with the mean unsigned error (MUE) below 5.5 cal mol-1 K-1 followed by sRRHO(100) and sRRHO with MUEs of 7.2 and 16.9 cal mol-1 K-1 . For the first time, we propose using the msRRHO scheme to calculate the enthalpy contribution that is further utilized to arrive at reaction Gibbs free energies (∆Gr ) ensuring the internal consistency. The final ∆Gr MUEs for msRRHO, sRRHO(100) and sRRHO schemes are 1.2, 3.6 and 3.1 kcal mol-1 .

Iron(II) Complexes with Porphyrin and Tetrabenzoporphyrin: CASSCF/MCQDPT2 Study of the Electronic Structures and UV-Vis Spectra by sTD-DFT.

The geometry and electronic structures of iron(II) complexes with porphyrin (FeP) and tetrabenzoporphyrin (FeTBP) in ground and low-lying excited electronic states are determined by DFT (PBE0/def2-TZVP) calculations and the complete active space self-consistent field (CASSCF) method, followed by the multiconfigurational quasi-degenerate second-order perturbation theory (MCQDPT2) approach to determine the dynamic electron correlation. The minima on the potential energy surfaces (PESs) of the ground (3A2g) and low-lying, high-spin (5A1g) electronic states correspond to the planar structures of FeP and FeTBP with D4h symmetry. According to the results of the MCQDPT2 calculations, the wave functions of the 3A2g and 5A1g electronic states are single determinant. The electronic absorption (UV-Vis) spectra of FeP and FeTBP are simulated within the framework of the simplified time-dependent density functional theory (sTDDFT) approach with the use of the long-range corrected CAM-B3LYP function. The most intensive bands of the UV-Vis spectra of FeP and FeTBP occur in the Soret near-UV region of 370-390 nm.

Ab initio calculations of the interaction potentials and thermodynamic functions for ArN and ArN.

Argon compounds play an important role in the mass spectrometry with inductively coupled plasma and other applications. At the same time, there is a little knowledge of their electronic terms and thermodynamic functions due to the complexity of experimental observations. In this work, the ab initio simulations are performed to obtain the interatomic interaction potentials for the ground and excited states of ArN and ArN+ . Using these potentials, the vibrational-rotational partition functions and thermodynamic properties in the gas phase are calculated for these molecules at the temperature range of 298.15-10,000 K. The errors of the thermodynamic functions associated with the approximation of interatomic interaction potentials are estimated.

Influence of the complete basis set approximation, tight weighted-core, and diffuse functions on the DLPNO-CCSD(T1) atomization energies of neutral H,C,O-compounds.

The impact of complete basis set extrapolation schemes (CBS), diffuse functions, and tight weighted-core functions on enthalpies of formation predicted via the DLPNO-CCSD(T1) reduced Feller-Peterson-Dixon approach has been examined for neutral H,C,O-compounds. All tested three-point (TZ/QZ/5Z) extrapolation schemes result in mean unsigned deviation (MUD) below 2 kJ mol-1 relative to the experiment. The two-point QZ/5Z and TZ/QZ CBS 1 / l max 3 extrapolation schemes are inferior to their inverse power counterpart ( 1 / l max + 1 / 2 4 ) by 1.3 and 4.3 kJ mol-1 . The CBS extrapolated frozen core atomization energies are insensitive (within 1 kJ mol-1 ) to augmentation of the basis set with tight weighted core functions. The core-valence correlation effects converge already at triple-ζ, although double-ζ/triple-ζ CBS extrapolation performs better and is recommended. The effect of diffuse function augmentation converges slowly, and cannot be reproduced with double- ζ or triple- ζ calculations as these are plagued with basis set superposition and incompleteness errors.

Physical and numerical aspects of sodium ion solvation free energies via the cluster-continuum model.

Sodium cation solvation Gibbs free energies (ΔGsolv(Na+)) have been obtained in water, dimethylformamide, dimethyl sulfoxide, ethanol, acetone, acetonitrile, and methanol through the "monomer cycle" cluster-continuum approach where a solvent reference state is described by infinitely separated molecules. The following steps are vital for obtaining reliable ΔGsolv(Na+) values: (a) a meticulous conformational search involving dispersion corrected density functional theory (DFT-D) and the continuum solvation model (CSM); (b) gas-phase DFT-D geometry optimization followed by single-point (SP) domain-based local pair natural orbital coupled clusters including single, double, and partly triple excitation (DLPNO-CCSD(T)) calculations in conjunction with the complete basis set extrapolation; (c) advanced statistical thermodynamic treatment of the low harmonic frequencies (<100 cm-1) to obtain the robust gas-phase Gibbs free energy correction; (d) gas-phase and dielectric continuum SP with non-electrostatic contributions included in the CSM; (e) an evaluation of the relative thermodynamic stability of the Na+(S)n clusters to identify the number of explicit solvent molecules n to be considered. Our refined computational protocol is promising with a Pearson correlation coefficient between the predicted and experimental data, ρ, of 0.82, and the mean signed and mean unsigned errors of 0.3 and 1.4 kcal mol-1, respectively.

Cluster-Continuum Model as a Sanity Check of Sodium Ions' Gibbs Free Energies of Transfer.

An approach to estimate the uncertainty of the calculated through the monomer cycle cluster-continuum model Gibbs free energy of transfer has been developed and suggested to be used as a quantitative measure of the reliability of the predictions. A set of experimental Na+ free energies of transfer from water to 18 solvents (ΔGtr(Na+, W → S)) has been assessed. For all solvents, we find Na+(S)n clusters to be thermodynamically unstable if n > 5. For 1,2-dichloroethane (1,2-DCIE), we have resolved considerable (ca. 10 kcal mol-1) discrepancies between available experimental ΔGtr(Na+, W → S). For 1,1-DCIE, we reject the only available experimental value and recommend our own estimate instead. We strongly propose experimental revisiting of ΔGtr(Na+, W → S) for ethylene glycol and hexamethylphosphoramide. The statistical analysis performed on a set of predicted and recommended experimental ΔGtr(Na+, W → S) values, in this work, results in the mean unsigned and signed deviations of 3.4 and -1.3 kcal mol-1, respectively. The squared Pearson correlation coefficient of 0.91 encourages the extension of the utilized theoretical approach to other available experimental data on ion solvation.

Gas-phase equilibrium molecular structures and ab initio thermochemistry of anthracene and rubrene.

Semi-experimental gas-phase structures of anthracene and rubrene (5,6,11,12-tetraphenyltetracene) were determined by means of gas electron diffraction (GED). The use of the flexible restraints in the refinement of the GED data successfully resolves non-equivalent C-C bond lengths. The tetracene core of an isolated rubrene molecule was found to exhibit a twist distortion of about 18°; this is less than DFT calculations predict (30-40°). The modified Feller-Peterson-Dixon method in conjunction with high-level DLPNO-CCSD(T) calculations was employed to resolve the discrepancy between the available experimental gas-phase enthalpies of formation for rubrene. The theoretical value of meets its recent experimental counterpart (765.6 ± 8.4 kJ mol-1) and is in strong disagreement with the previous estimation (882 kJ mol-1).

Conformational energies of microsolvated Na+ clusters with protic and aprotic solvents from GFNn-xTB methods.

Performance of contemporary tight-binding semiempirical GFNn-xTB methods for the conformational energies of singly charged sodium clusters Na+ (S)n (n = 4-8) with 3 protic and 8 aprotic solvents is examined against the reference RI-MP2/CBS method. The median Pearson correlation coefficients of ρ = 0.84 (GFN2-xTB) and ρ = 0.82 (GFN1-xTB) do not give the clear preference to any tested approach. GFN1-xTB method demonstrates more stable performance than its GFN2-xTB successor with the average mean absolute errors (MAEs)/mean signed errors (MSEs) of 1.2/0.2 and 2.3/1.6 kcal mol-1 , respectively. Conformational energies produced by the computationally efficient DFT functional PBE and double-ζ basis set complemented with -D3(BJ) dispersion correction are suitable for the preliminary sampling (median ρ = 0.93), but should be used with a caution for the calculations of the average ensemble properties (MAE/MSE = 1.7/1.1 kcal mol-1 ). Higher-ranking PBE0-D3(BJ) and ωB97M-V with triple-ζ basis sets yield significantly lower MAEs/MSEs of 0.55/0.20 and 0.51/0.23 kcal mol-1 , respectively.

16OSTM10: a new open-shell transition metal conformational energy database to challenge contemporary semiempirical and force field methods.

A new database, 16OSTM10, containing 10 conformations for each of 16 non-multireference realistic-size open-shell transition metal (OSTM) complexes has been developed. Contemporary composite density functional theory (DFT) (PBEh-3c and B97-3c), semiempirical (PM6 and PM7) and the GFNn-xTB/FF family methods were examined against conventional DFT (PBE-D3(BJ), PBE0-D3(BJ), M06 and ωB97X-V) to reproduce the conformational energies. While good performance is observed for the conventional (the average Pearson correlation coefficient is ρ = 0.91) and composite DFT (average ρ = 0.93), semiempirical and force-field methods should still be used with caution for these challenging compounds. The corresponding average ρ values are 0.53 (PM6 and PM7), 0.75 (GFN1-xTB and GFN2-xTB) and 0.62 (GFN-FF). Accounting for the intramolecular dispersion interactions turned out to be crucial for 4 OSTM complexes bearing bulky substituents in close proximity to each other. The influence of the scalar relativistic effects on the conformational energies is negligible for the considered 3d metal species.

"In Vitro" and "In Vivo" Diagnostic Check for the Thermochemistry of Metal-Organic Compounds.

Volatile metal ß-diketonates are of interest from both practical and theoretical perspectives (manufacturing of film materials, catalysis, and the nature of metal-ligand bonding). Knowledge of their reliable thermochemical properties is essential for effective applications. However, there is an unacceptable scattering of the available data on the enthalpies of formation. In this work, we proposed "in vitro" and "in vivo" diagnostic tools to verify the available enthalpies of formation in both the crystalline and gaseous states for metal tris-ß-diketonates. The "in vitro" procedure involved high-level quantum-chemical calculations and was applied to define a consistent data set on the enthalpies of formation for iron(III) ß-diketonates. This data set has provided the basis for "in vivo" structure-property-based diagnostics to evaluate the robustness of the thermochemical data for ß-diketonate tris-complexes with metals other than iron.

Gas-phase thermochemistry of polycyclic aromatic hydrocarbons: an approach integrating the quantum chemistry composite scheme and reaction generator.

We introduce a protocol aimed at predicting the accurate gas-phase enthalpies of formation of polycyclic aromatic hydrocarbons (PAHs). Automatic generation of a dataset of equilibrated chemical reactions preserving the number of carbon atoms in each hybridization state on each side of equations is at the core of our scheme. The performed tests suggest the recommended enthalpy of formation to be derived via a two-step scheme. First, we consider the reactions with a minimal sum of the total number of particles involved, N, and the absolute difference between the total number of products and reactants, |ΔN|. Second, among these reactions, we identify the one with the smallest absolute reaction enthalpy change, . This approach has been applied to predict the gas-phase enthalpies of formation of 113 PAHs via the Feller-Peterson-Dixon approach. Our calculated values provide the mean absolute deviations of 1.7, 1.9, 4.2, 8.1, and 18.5 kJ mol-1 with respect to the literature group-based error corrected (GBEC) G3MP2B3, ATOMIC (HC), group equivalent M06-2X, GBEC B3LYP, and G4MP2 values. Our predicted values give the mean signed and mean absolute errors of -7.5 and 12.9 kJ mol-1 with respect to the experimental enthalpies of formation. The combination of our predicted and the experimental values provide the solid-state enthalpies of formation, , which are not available for a few species. Approaching these values as well as , producing large discrepancies from the experimental side, would be indispensable for testing and further tuning of computational chemistry approaches.

Ambiguities in solvation free energies from cluster-continuum quasichemical theory: lithium cation in protic and aprotic solvents.

Gibbs free energies for Li+ solvation in water, methanol, acetonitrile, DMSO, dimethylacetamide, dimethoxyethane, dimethylformamide, gamma-butyrolactone, pyridine, and sulfolane have been calculated using the cluster-continuum quasichemical theory. With n independent solvent molecules S initial state forming the "monomer" thermodynamic cycle, Li+ solvation free energies are found to be on average 14 kcal mol-1 more positive compared to those from the "cluster" thermodynamic cycle where the initial state is the cluster Sn. We ascribe the inconsistency between the "monomer" and "cluster" cycles mainly to the incorrectly predicted solvation free energies of solvent clusters Sn from the SMD and CPCM continuum solvation models, which is in line with the earlier study of Bryantsev et al., J. Phys. Chem. B, 2008, 112, 9709-9719. When experimental-based solvation free energies of individual solvent molecules and solvent clusters are employed, the "monomer" and "cluster" cycles result in identical numbers. The best overall agreement with experimental-based "bulk" scale lithium cation solvation free energies was obtained for the "monomer" scale, and we recommend this set of values. We expect that further progress in the field is possible if (i) consensus on the accuracy of experimental reference values is achieved; (ii) the most recent continuum solvation models are properly parameterized for all solute-solvent combinations and become widely accessible for testing.

Molecular Structure of Nickel Octamethylporphyrin-Rare Experimental Evidence of a Ruffling Effect in Gas Phase.

The structure of a free nickel (II) octamethylporphyrin (NiOMP) molecule was determined for the first time through a combined gas-phase electron diffraction (GED) and mass spectrometry (MS) experiment, as well as through quantum chemical (QC) calculations. Density functional theory (DFT) calculations do not provide an unambiguous answer about the planarity or non-planar distortion of the NiOMP skeleton. The GED refinement in such cases is non-trivial. Several approaches to the inverse problem solution were used. The obtained results allow us to argue that the ruffling effect is manifested in the NiOMP molecule. The minimal critical distance between the central atom of the metal and nitrogen atoms of the coordination cavity that provokes ruffling distortion in metal porphyrins is about 1.96 Å.

Gas-Phase Thermochemistry of MX3 and M2X6 (M = Sc, Y; X = F, Cl, Br, I) from a Composite Reaction-Based Approach: Homolytic versus Heterolytic Cleavage.

A domain-based local-pair natural-orbital coupled-cluster approach with single, double, and improved linear-scaling perturbative triple correction via an iterative algorithm, DLPNO-CCSD(T1), was applied within the framework of the Feller-Peterson-Dixon approach to derive gas-phase heats of formation of scandium and yttrium trihalides and their dimers via a set of homolytic and heterolytic dissociation reactions. All predicted heats of formation moderately depend on the reaction type with the most and least negative values obtained for homolytic and heterolytic dissociation, respectively. The basis set size dependence, as well as the influence of static correlation effects not covered by the standard (DLPNO-)CCSD(T) approach, suggests that exploitation of the heterolytic dissociation reactions with the formation of M3+ and X- ions leads to the most robust heats of formation. The gas-phase formation enthalpies ΔHf°(0 K)/ΔHf°(298.15 K) and absolute entropies S°(298.15 K) were obtained for the first time for the Sc2F6, Sc2Br6, and Sc2I6 species. For ScBr3, ScI3, Sc2Cl6, and Y2Cl6, we suggest a reexamination of the experimental heats of formation available in the literature. For other compounds, the predicted values were found to be in good agreement with the experimental estimates. Extracted MX3 (M = Sc, Y; X = F, Cl, Br, and I) 0 K atomization enthalpies indicate weaker bonding when moving from fluorine to iodine and from yttrium to scandium. Likewise, the stability of yttrium trihalide dimers degrades when going from fluorine to iodine. Respective scandium trihalide dimers are less stable, with 0 K dimer dissociation energy decreasing in the row fluorine - chlorine - bromine ≈ iodine. Correlation of the (n - 1)s2p6 electrons on bromine and iodine, inclusion of zero-point energy, relativistic effects, and the effective-core-potential correction as well as amelioration of the DLPNO localization inaccuracy are shown to be of similar magnitude, which is critical if accurate heats of formation are a goal.

Mechanistic Insight into the Photoredox-Nickel-HAT Triple Catalyzed Arylation and Alkylation of α-Amino Csp3-H Bonds.

We report here a comprehensive computational analysis of the mechanisms of the photoredox-nickel-HAT (HAT: hydrogen atom transfer) catalyzed arylation and alkylation of α-amino Csp3-H bonds developed by MacMillan and co-workers. Different alternatives for the three catalytic cycles were tested to identify unambiguously the operative reaction mechanism. Our analysis indicated that the IrIII photoredox catalyst, upon irradiation with visible light, can be either reduced or oxidized by the HAT and nickel catalysts, respectively, indicating that both reductive and oxidative quenching catalytic cycles can be operative, although the reductive cycle is favored. Our analysis of the HAT cycle indicated that activation of a α-amino Csp3-H bond of the substrate is facile and selective relative to activation of a ß-amino Csp3-H bond. Finally, our analysis of the nickel cycle indicated that both arylation and alkylation of α-amino Csp3-H bonds occurs via the sequence of nickel oxidation states NiI-NiII-NiI-NiIII and of elementary steps: radical addition-SET-oxidative addition-reductive elimination.

Evaluation of experimental alkali metal ion-ligand noncovalent bond strengths with DLPNO-CCSD(T) method.

We applied the domain based local pair natural orbital coupled cluster approach with single, double, and perturbative triple excitations, DLPNO-CCSD(T), to rationalize more than 130 experimental bond dissociation enthalpies collected in the work of Rodgers and Armentrout [Chem. Rev. 116, 5642-5687 (2016)] and involving alkali metal cations and versatile neutral organic and inorganic ligands ranging from common solvents to amino acids. In general, a remarkable agreement has been obtained between predicted and experimental alkali metal ion-ligand noncovalent bond strengths, highlighting a high degree of reliability of data assembled by Rodgers and Armentrout. In the case of some inconsistent experimental data given for some species, we pointed to a number for which best agreement with DLPNO-CCSD(T) calculations has been achieved. In addition, we refined a couple of ΔH0 for which DLPNO-CCSD(T) values turned out to be significantly different from their experimental counterparts. We suggest an application of the DLPNO-CCSD(T) to derive the reference values to train/validate force field and neural network methods to be further applied in molecular dynamic simulations to unravel the mechanisms in biological systems and alkali metal ion batteries.

Gas Phase Silver Thermochemistry from First Principles.

Domain-based local pair natural orbital coupled cluster approach with single, double, and perturbative triple excitations, DLPNO-CCSD(T), has been applied within a framework of a reduced version of the reaction-based Feller-Peterson-Dixon (FPD) scheme to predict gas phase heats of formation and absolute entropies of silver inorganic and organometallic compounds. First, we evaluated all existing experimental data currently limited by thermodynamic functions of 10 silver substances (AgH, AgF, AgBr, AgI, Ag2, Ag2S, Ag2Se, Ag2Te, AgCN, AgPO2). The mean average deviation between computed and experimental heats of formation was found to be 1.9 kcal/mol. Notably, all predicted heats of formation turned out to be within the error bounds of their experimental counterparts. Second, we predicted heats of formation and entropies for additional 90 silver species with no experimental data available, substantially enriching silver thermochemistry. Combination of gas phase heats of formation Δ Hf and entropies S° of AgNO2, AgSCN, Ag2SO4, and Ag2SeO4 obtained in this work, with respective solid-state information, resulted in accurate sublimation thermochemistry of these compounds. Complementation of predicted Δ Hf with heats of formation of some neutrals and positive ions produced 33 silver bond strengths of high reliability. Obtained thermochemical data are promising for developing the concepts of silver chemistry. In addition, derived heats of formation and bond dissociation enthalpies, due to their high diversity, are found to be relevant for testing and training of computational chemistry methods.