The Perfluoro-o-phenylene-mercury Trimer [Hg(o-C6F4)]3 - a Textbook Example of Phase-Dependent Structural Differences.

The geometric and electronic structure of [Hg(o-C6F4)]3 (1) in the gas phase, i.e. free of intermolecular interactions, was deter-mined by a synchronous gas-phase electron diffraction/mass spec-trometry experiment (GED/MS), complemented by quantum chemi-cal calculations. 1 is stable up to 498 K and the gas phase contains a single molecular form: the trimer [Hg(o-C6F4)]3. It has a planar structure of D3h sym-metry with a Hg-C distance of 2.075(5) Å and a Hg-Hg distance of 3.614(7) Å (both rh1). Structural differences between the crystalline and gaseous state have been analyzed. Different DFT functio-nal-basis combi-na-tions were tested, demon-stra-ting the importance to consider the relativistic effects of the mercury atoms. The combi-na-tion PBE0/-MWB(Hg),cc-pVTZ(C,F) turned out to be the most appro-priate for the geometry optimization of such organomercurials. The elec-tronic structure of 1, the nature of the chemical bonding in C-Hg-C fragments and the nature of the Hg···Hg inter-actions have been analyzed in terms of the Natural Bond Orbital (NBO) and Quantum Theory of Atoms in Molecules (QTAIM) approaches. The influence of the nature of halogen substi-tution on the structure of the molecules in the series [Hg(o-C6H4)]3, [Hg(o-C6F4)]3, [Hg(o-C6Cl4)]3, [Hg(o-C6Br4)]3 was also analyzed.

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.

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 .

Accurate single crystal and gas-phase molecular structures of acenaphthene: a starting point in the search for the longest C-C bond.

The molecular structure of acenaphthene has been determined experimentally in the gas phase using gas electron diffraction intensities and literature-available rotational constants. Supplementary high-level quantum-chemical calculations were utilized in refinements of the semi-empirical equilibrium structure. In this work we investigate on how different schemes of GED data averaging and weighting can be used for obtaining the most accurate and precise structural parameters. Single-crystal X-ray diffraction experiments at different temperatures have been performed and the solid-state structure of acenaphthene has been determined. Both gas and solid-state acenaphthene molecules are planar and possess a non-twisted ethylene bridge. The aliphatic C-C bond in the ethylene fragment is elongated to 1.560(4) Å in the gas phase and 1.5640(4) Å in the solid phase. Based on the experimental data several theoretical approximations have been calibrated and predictions for other molecules were made, taking into account dispersion and electrostatic interactions. Particular derivatives of acenaphthene may potentially have significantly elongated C-C bonds up to 1.725 Å. However, among the experimental gas-phase structures available to date probably the longest C-C bond (re,(av) = 1.750(28) Å at w = 0.93) was determined in a carbaborane derivative 1,2-(SeH)2-closo-1,2-C2B10H10.

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.

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.

DFT Study of the Molecular and Electronic Structure of Metal-Free Tetrabenzoporphyrin and Its Metal Complexes with Zn, Cd, Al, Ga, In.

The electronic and molecular structures of metal-free tetrabenzoporphyrin (H2TBP) and its complexes with zinc, cadmium, aluminum, gallium and indium were investigated by density functional theory (DFT) calculations with a def2-TZVP basis set. A geometrical structure of ZnTBP and CdTBP was found to possess D4h symmetry; AlClTBP, GaClTBP and InClTBP were non-planar complexes with C4v symmetry. The molecular structure of H2TBP belonged to the point symmetry group of D2h. According to the results of the natural bond orbital (NBO) analysis, the M-N bonds had a substantial ionic character in the cases of the Zn(II) and Cd(II) complexes, with a noticeably increased covalent contribution for Al(III), Ga(III) and In(III) complexes with an axial -Cl ligand. The lowest excited states were computed with the use of time-dependent density functional theory (TDDFT) calculations. The model electronic absorption spectra indicated a weak influence of the nature of the metal on the Q-band position.

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.

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.

Molecular Structure of Pyrazinamide: A Critical Assessment of Modern Gas Electron Diffraction Data from Three Laboratories.

Accuracy and precision of molecular parameters determined by modern gas electron diffraction have been investigated. Diffraction patterns of gaseous pyrazinamide have been measured independently in three laboratories, in Bielefeld (Germany), Ivanovo (Russia), and Moscow (Russia). All data sets have been analyzed in equal manner using a highly controlled background elimination procedure and flexible restraints in molecular structure refinement. In detailed examination and comparison of the obtained results we have determined the average experimental precision of 0.004 Å for bond lengths and 0.2° for angles. The corresponding average deviations of the refined parameters from the ae-CCSD(T)/cc-pwCVTZ theoretical values were 0.003 Å and 0.2°. The average precision for refined amplitudes of interatomic vibrations was determined to be 0.005 Å. It is recommended to take into account these values in calculations of total errors for refined parameters of other molecules with comparable complexity.

DFT Study of Molecular and Electronic Structure of Ca(II) and Zn(II) Complexes with Porphyrazine and tetrakis(1,2,5-thiadiazole)porphyrazine.

Electronic and geometric structures of Ca(II) and Zn(II) complexes with porphyrazine (Pz) and tetrakis(1,2,5-thiadiazole)porphyrazine (TTDPz) were investigated by density functional theory (DFT) calculations and compared. The perimeter of the coordination cavity was found to be practically independent on the nature of a metal and a ligand. According to the results of the natural bond orbital (NBO) analysis and quantum theory of atoms in molecules (QTAIM) calculations, Ca-N bonds possess larger ionic contributions as compared to Zn-N. The model electronic absorption spectra obtained with the use of time-dependent density functional theory (TDDFT) calculations indicate a strong bathochromic shift (~70 nm) of the Q-band with a change of Pz ligand by TTDPz for both Ca and Zn complexes. Additionally, CaTTDPz was synthesized and its electronic absorption spectrum was recorded in pyridine and acetone.

Ligand Coordination in Bis(ß-diketonato) d Metals: The Mn(II) Case of D2 h versus D2 d Symmetry.

The structure of free manganese(II) bis-acetylacetonate [Mn(acac)2] was determined experimentally by gas-phase electron diffraction. The vapor at 197(5) °C is composed of a single conformer of Mn(acac)2 in D2 d symmetry with a central structural motif of an elongated MnO4 tetrahedron with a Mn-O distance ( re) of 2.035(5) Å and a bond angle in chelate rings (∠O-Mn-O) of 89.4(6)°. This result contradicts the predicted planar structure of the MO4 moiety ( D2 h) with a short Mn-O distance ( re) of 1.771 Å from a MC(5i5)QDPT2 calculation. From these findings and by comparison with data from the literature, we conclude that in general in bis(ß-diketonato) coordination compounds of d metals there is a perpendicular arrangement of the two ligands for d0, d5, and d10 coordination centers and a planar arrangement ( D2 h) for others.

Nitroxoline Molecule: Planar or Not? A Story of Battle between π-π Conjugation and Interatomic Repulsion.

The conformational properties of the nitro group in nitroxoline (8-hydroxy-5-nitroquinoline, NXN) were investigated in the gas phase by means of gas electron diffraction (GED) and quantum chemical calculations, and also with solid-state analysis performed using terahertz time-domain spectroscopy (THz-TDS). The results of the GED refinement show that in the equilibrium structure the NO2 group is twisted by angle ϕ = 8 ± 3° with respect to the 8-hydroxyoquinoline plane. This is the result of interatomic repulsion of oxygen in the NO2 group from the closest hydrogen, which overcomes the energy gain from the π-π conjugation of the nitro group and aromatic system of 8-hydroxyoquinoline. The computation of equilibrium geometry using MP2/cc-pVXZ (X = T, Q) shows a large overestimation of the ϕ value, while DFT with the cc-pVTZ basis set performs reasonably well. On the other hand, DFT computations with double-ζ basis sets yield a planar structure of NXN. The refined potential energy surface of the torsion vibration the of nitro group in the condensed phase derived from the THz-TDS data indicates the NXN molecule to be planar. This result stays in good agreement with the previous X-ray structure determination. The strength of the π-system conjugation for the NO2 group and 8-hydroxyoquinoline is discussed using NBO analysis, being further supported by comparison of the refined semiexperimental gas-phase structure of NXN from GED with other nitrocompounds.

Gas-phase structure of 1,8-bis[(trimethylsilyl)ethynyl]anthracene: cog-wheel-type vs. independent internal rotation and influence of dispersion interactions.

The gas-phase structure of 1,8-bis[(trimethylsilyl)ethynyl]anthracene (1,8-BTMSA) was determined by a combined gas electron diffraction (GED)/mass spectrometry (MS) experiment as well as by quantum-chemical calculations (QC). DFT and dispersion corrected DFT calculations (DFT-D3) predicted two slightly different structures for 1,8-BTMSA concerning the mutual orientation of the two -C-C[triple bond, length as m-dash]C-SiMe3 units: away from one another or both bent to the same side. An attempt was made to distinguish these structures by GED structural analysis. To probe the structural rigidity, a set of Born-Oppenheimer molecular dynamics (BOMD) calculations has been performed at the DFT-D level. Vibrational corrections Δr = ra - re were calculated by two BOMD approaches: a microcanonically (NVE) sampled ensemble of 20 trajectories (BOMD(NVE)) and a canonical (NVT) trajectory thermostated by the Noose-Hoover algorithm (BOMD(NVT)). In addition, the conventional approach with both, rectilinear and curvilinear approximations (SHRINK program), was also applied. Radial distribution curves obtained with models using both MD approaches provide a better description of the experimental data than those obtained using the rectilinear (SHRINK) approximation, while the curvilinear approach turned out to lead to physically inacceptable results. The electronic structure of 1,8-BTMSA was investigated in terms of an NBO analysis and was compared with that of the earlier studied 1,8-bis(phenylethynyl)anthracene. Theoretical and experimental results lead to the conclusion that the (trimethylsilyl)ethynyl (TMSE) groups in 1,8-BTMSA are neither restricted in rotation nor in bending at the temperature of the GED experiment.

The effect of molecular dynamics sampling on the calculated observable gas-phase structures.

In this study, we compare the performance of various ab initio molecular dynamics (MD) sampling methods for the calculation of the observable vibrationally-averaged gas-phase structures of benzene, naphthalene and anthracene molecules. Nose-Hoover (NH), canonical and quantum generalized-Langevin-equation (GLE) thermostats as well as the a posteriori quantum correction to the classical trajectories have been tested and compared to the accurate path-integral molecular dynamics (PIMD), static anharmonic vibrational calculations as well as to the experimental gas electron diffraction data. Classical sampling methods neglecting quantum effects (NH and canonical GLE thermostats) dramatically underestimate vibrational amplitudes for the bonded atom pairs, both C-H and C-C, the resulting radial distribution functions exhibit nonphysically narrow peaks. This deficiency is almost completely removed by taking the quantum effects on the nuclei into account. The quantum GLE thermostat and a posteriori correction to the canonical GLE and NH thermostatted trajectories capture most vibrational quantum effects and closely reproduce computationally expensive PIMD and experimental radial distribution functions. These methods are both computationally feasible and accurate and are therefore recommended for calculations of the observable gas-phase structures. A good performance of the quantum GLE thermostat for the gas-phase calculations is encouraging since its parameters have been originally fitted for the condensed-phase calculations. Very accurate molecular structures can be predicted by combining the equilibrium geometry obtained at a high level of electronic structure theory with vibrational amplitudes and corrections calculated using MD driven by a lower level of electronic structure theory.