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Iron(II) phthalocyanine (FePc) is an important member of the phthalocyanines family with potential applications in the fields of electrocatalysis, magnetic switching, electrochemical sensing, and phototheranostics. Despite the importance of electronic properties of FePc in these applications, a reliable determination of its ground-state is still challenging. Here we present combined state of the art computational methods and experimental approaches, that is, Mössbauer spectroscopy and Superconducting Quantum Interference Device (SQUID) magnetic measurements to identify the ground state of FePc. While the nature of the ground state obtained with density functional theory (DFT) depends on the functional, giving mostly the triplet state, multi-reference complete active space second-order perturbation theory (CASPT2) and density matrix renormalization group (DMRG) methods assign quintet as the FePc ground-state in gas-phase. This has been confirmed by the hyperfine parameters obtained from 57 Fe Mössbauer spectroscopy performed in frozen monochlorobenzene. The use of monochlorobenzene guarantees an isolated nature of the FePc as indicated by a zero Weiss temperature. The results open doors for exploring the ground state of other metal porphyrin molecules and their controlled spin transitions via external stimuli.

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Interaction energies computed with density functional theory can be divided into physically meaningful components by symmetry-adapted perturbation theory (DFT-SAPT) or the canonical energy decomposition analysis (EDA). In this work, the decomposition results obtained by these schemes were compared for more than 200 hydrogen-, halogen-, and pnicogen-bonded, dispersion-bound, and mixed complexes to investigate their similarity in the evaluation of the nature of noncovalent interactions. BLYP functional with D3(BJ) correction was used for the EDA scheme, whereas asymptotically corrected PBE0 functional for DFT-SAPT provided some of the best combinations for description of noncovalent interactions. Both schemes provide similar results concerning total interaction energies and insight into the individual energy components. For most complexes, the dominant energetic term was identified equally by both decomposition schemes. Because the canonical EDA is computationally less demanding than the DFT-SAPT, the former can be especially used in cases where the systems investigated are very large.

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The stability of the T-shaped and stacked complexes of benzene with methanethial (CH2S) and methaneselone (CH2Se) and their difluoro-, dichloro-, dibromo-derivatives is investigated in their ground and first electronic excited states by means of the SCS-ADC2 method. The origin of the stabilization in the ground state is discussed based on the results of calculations performed using the DFT-SAPT method. Calculations show that the stability of the T-shaped conformers increases upon electronic excitation, while it decreases for most of the stacked conformers. Both effects are explained by the changes in the electrostatic potential (ESP) of isolated monomers upon the electronic excitation.

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Close B-Hπ contacts have recently been observed in crystallographic structures of Ir-dithiolene-phosphine complexes containing boron hydride cluster. This finding was interpreted using quantum chemical calculations as a new type of electrostatically driven nonclassical hydrogen bonding. However, such an explanation contradicts the wealth of evidence for unique noncovalent interactions of boron hydrides. Moreover, care must be exercised when computational methods are used to interpret new phenomena. Therefore, here, we cautiously examine the B-Hπ interaction by means of advanced quantum chemistry and disprove the claimed attractive electrostatic nature and rather define it as a nonspecific dispersion-driven contact. In summary, we present evidence that the crystallographically observed B-Hπ contacts do not constitute a novel type of hydrogen bonding of boron hydride clusters.

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In density functional theory-based symmetry-adapted perturbation theory (DFT-SAPT) interaction energy calculations, the most demanding step is the calculation of the London dispersion term. For this bottleneck to be avoided and DFT-SAPT to be made applicable to larger systems, the ab initio dispersion terms can be replaced by one calculated empirically at an almost negligible cost ( J. Phys. Chem. A 2011 ; 115 , 11321 - 11330 ). We present an update of this approach that improves accuracy and makes the method applicable to a wider range of systems. It is based on Grimme's D3 dispersion correction for DFT, where the damping function is changed to one suitable for the calculation of the complete dispersion energy. The best results have been achieved with the Tang-Toennies damping function. It has been parametrized on the S66×8 data set for which we report density fitting DFT-SAPT/aug-cc-pVTZ interaction energy decomposition. The method has been validated on a diverse set of noncovalent systems including difficult cases such as very compact noncovalent complexes of charge-transfer type. The root-mean-square errors in the complete test set are 0.73 and 0.42 kcal mol-1 when charge-transfer complexes are excluded. The proposed empirical dispersion terms can also be used outside the DFT-SAPT framework, e.g., for the estimation of the amount of dispersion in a calculation where only the total interaction energy is known.

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The strength and nature of the connection in Lappert's stannylene dimer ({Sn[CH(SiMe3)2]2}2) and its smaller analogs, simplified stannylenes, as well as similar Ge complexes were studied by means of DFT-D3 calculations, energy decomposition analysis (EDA), electrostatic potential (ESP), and natural population analysis. The trans-bent structure of the investigated molecules was rationalized by means of EDA, ESP, and molecular orbital (MO) analyses. The different ESPs for the monomers studied are a result of different hybridization of the Sn (Ge) atoms. The comparably strong stabilization in the largest and the smallest systems with a dramatically different substituent size is explained by the different nature of the binding between monomers. For all complexes, it has been found that the total attractive interaction is mostly provided by the electrostatic component (>50%), followed by orbital interaction and dispersion. In the largest molecule (Lappert's stannylene), the dispersion interaction plays a more significant role in stabilization and its magnitude is comparable to that of orbital interaction; on the other hand in the smallest molecule (SnH2), where bulky substituents are replaced by H only, the dispersion energy is less important and the E-E bond is more of a charge-transfer character, caused by donor-acceptor orbital interactions. The charge transfer in Ge dimers is greater than in the Sn ones due to shorter distances between monomers, which cause better ⟨HOMO/LUMO⟩ overlaps. The easier dimerization of Lappert's stannylene as compared to Kira's ({Sn[(Me3Si)2CHCH2CH2CH(SiMe3)2-κ(2)C,C']}) stannylene is explained by the different orientation of their substituents-asymmetry promotes dimerization.

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The non-planarity of the benzene moiety in the crystal of a chelated bismuth(iii) heteroboroxine complex was not supported by DFT-D quantum chemical calculations. The observed bent structure of benzene is in fact a superimposition (thermal average) of the ensemble of thermally populated benzene structures in the complex studied.

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The effect of polar flattening on the stability of 32 halogen-bonded complexes was investigated by utilizing CCSD(T)/CBS, DFT, and DFT-SAPT/CBS methods. It is shown that the value of polar flattening increases with the decreasing value of studied isodensity. For the complexes investigated, the polar flattening based on the isodensity of 0.001 au reaches 0.2-0.3 Å and 10-15% in absolute and relative values, respectively. These geometrical changes induce differences in the stabilization energy up to 20%.

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The reduction of N,C,N-chelated bismuth chlorides [C6H3-2,6-(CH=NR)2]BiCl2 [where R = tBu (1), 2',6'-Me2C6H3 (2), or 4'-Me2NC6H4 (3)] or N,C-chelated analogues [C6H2-2-(CH=N-2',6'-iPr2C6H3)-4,6-(tBu)2]BiCl2 (4) and [C6H2-2-(CH2NEt2)-4,6-(tBu)2]BiCl2 (5) is reported. Reduction of compounds 1-3 gave monomeric N,C,N-chelated bismuthinidenes [C6H3-2,6-(CH=NR)2]Bi [where R = tBu (6), 2',6'-Me2C6H3 (7) or 4'-Me2NC6H4 (8)]. Similarly, the reduction of 4 led to the isolation of the compound [C6H2-2-(CH=N-2',6'-iPr2C6H3)-4,6-(tBu)2]Bi (9) as an unprecedented two-coordinated bismuthinidene that has been structurally characterized. In contrast, the dibismuthene {[C6H2-2-(CH2NEt2)-4,6-(tBu)2]Bi}2 (10) was obtained by the reduction of 5. Compounds 6-10 were characterized by using (1)H and (13)C NMR spectroscopy and their structures, except for 7, were determined with the help of single-crystal X-ray diffraction analysis. It is clear that the structure of the reduced products (bismuthinidene versus dibismuthene) is ligand-dependent and particularly influenced by the strength of the N→Bi intramolecular interaction(s). Therefore, a theoretical survey describing the bonding situation in the studied compounds and related bismuth(I) systems is included. Importantly, we found that the C3NBi chelating ring in the two-coordinated bismuthinidene 9 exhibits significant aromatic character by delocalization of the bismuth lone pair.

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Five different structures (L- and T-shaped (LS, TS), parallel (P), parallel-displaced (PD), and linear (L)) of (X2)2 dimers (X = F, Cl, Br, I, N) have been investigated at B97-D3, M06-2X, DFT-SAPT, and CCSD(T) levels. The Qzz component of the quadrupole moment of all dihalogens, which coincides with the main rotational axis of the symmetry of the molecule, has been shown to be positive, whereas that of dinitrogen is negative. All of these values correlate well with the most positive value of the electrostatic potential, which, for dihalogens, reflects the magnitude of the σ-hole. The LS structure is the most stable structure for all dihalogen dimers. This trend is the most pronounced in the case of iodine and bromine; for dinitrogen dimer, the LS, TS, and PD structures are comparably stable. The dominant stabilization energy for dihalogen dimers is dispersion energy, followed by Coulomb energy. In the case of dinitrogen dimer, it is only the dispersion energy. At short distances, the Coulomb (polarization) energy for dihalogen dimers is more attractive for the LS structure; at larger distances, the TS structure is more favorable, as dispersion and induction energies are systematically more stable for the TS structure. For all dimers and all distances, the long-range electrostatic energy covering the interactions of multipole moments is the most attractive for the TS structure. In the case of dihalogen dimers, the preference of the LS structure over the others, resulting from the concert action of Coulomb, dispersion, and induction energies, is explained by the presence of a σ-hole. In the case of dinitrogen, comparable stability of LS, TS, and PD structures is obtained, as all are dominantly stabilized by dispersion energy.

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The stabilisation energies of the crystal structures of 1,3-dithiole-2-thione-4-carboxyclic acid···I2 and DABCO···I2 complexes determined by the CCSD(T)/CBS method are very large and exceed 8 and 15 kcal mol(-1), respectively. The DFT-D method (B97-D3/def2-QZVP) strongly overestimates these stabilisation energies, which support the well-known fact that the DFT-D method is not very applicable to the study of charge-transfer complexes. On the other hand, the M06-2X/def2-QZVP method provides surprisingly reliable energies. A DFT-SAPT analysis has shown that a substantial stabilisation of these complexes arises from the charge-transfer energy included in the induction energy and that the respective induction energy is much larger than that of other non-covalently bound complexes. The total stabilisation energies of the complexes mentioned as well as of those where iodine has been replaced by lighter halogens (Br2 and Cl2) or by hetero systems (IF, ICH3, N2) correlate well with the magnitude of the σ-hole (Vs,max value) as well as with the LUMO energy. The nature of the stabilisation of all complexes between both electron donors and X2 (X = I, Br, Cl, N) systems is explained by the magnitude of the σ-hole but surprisingly also by the values of the electric quadrupole moment of these systems. Evidently, the nature of the stabilisation of halogen-bonded complexes between electron donors and systems where the first non-zero electric multipole moment is the quadrupole moment can be explained not only by the recently introduced concept of the σ-hole but also by the classical concept of electric quadrupole moments.

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We evaluate the performance of the most widely used wavefunction, density functional theory, and semiempirical methods for the description of noncovalent interactions in a set of larger, mostly dispersion-stabilized noncovalent complexes (the L7 data set). The methods tested include MP2, MP3, SCS-MP2, SCS(MI)-MP2, MP2.5, MP2.X, MP2C, DFT-D, DFT-D3 (B3-LYP-D3, B-LYP-D3, TPSS-D3, PW6B95-D3, M06-2X-D3) and M06-2X, and semiempirical methods augmented with dispersion and hydrogen bonding corrections: SCC-DFTB-D, PM6-D, PM6-DH2 and PM6-D3H4. The test complexes are the octadecane dimer, the guanine trimer, the circumcoronene…adenine dimer, the coronene dimer, the guanine-cytosine dimer, the circumcoronene…guanine-cytosine dimer, and an amyloid fragment trimer containing phenylalanine residues. The best performing method is MP2.5 with relative root mean square deviation (rRMSD) of 4 %. It can thus be recommended as an alternative to the CCSD(T)/CBS (alternatively QCISD(T)/CBS) benchmark for molecular systems which exceed current computational capacity. The second best non-DFT method is MP2C with rRMSD of 8 %. A method with the most favorable "accuracy/cost" ratio belongs to the DFT family: BLYP-D3, with an rRMSD of 8 %. Semiempirical methods deliver less accurate results (the rRMSD exceeds 25 %). Nevertheless, their absolute errors are close to some much more expensive methods such as M06-2X, MP2 or SCS(MI)-MP2, and thus their price/performance ratio is excellent.

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The crystals of benzene and hexahalogenbenzenes have been studied by means of the density functional theory augmented by an empirical dispersion correction term as well as by the symmetry-adapted perturbation theory. In order to elucidate the nature of noncovalent binding, pairwise interactions have been investigated. It has been demonstrated that the structures of dimers with the highest stabilization energy differ notably along the crystals. It has been shown that the differences in the experimental sublimation energies might be attributed to the dispersion interaction. To our surprise, the dihalogen bonding observed in the hexachloro- and hexabromobenzenes plays a rather minor role in structure stabilization because it is energetically comparable with the other binding motifs. However, the dihalogen bond is by far the most frequent binding motif in hexachloro- and hexabromobenzenes.

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The performance of the second-order Møller-Plesset perturbation theory MP2.5 and MP2.X methods, tested on the S22, S66, X40, and other benchmark datasets is briefly reviewed. It is found that both methods produce highly accurate binding energies for the complexes contained in these data sets. Both methods also provide reliable potential energy curves for the complexes in the S66 set. Among the routinely used wavefunction methods, the only other technique that consistently produces lower errors, both for stabilization energies and geometry scans, is the spin-component-scaled coupled-clusters method covering iterative single- and double-electron excitations, which is, however, substantially more computationally intensive. The structures originated from full geometrical gradient optimizations at the MP2.5 and MP2.X level of theory were confirmed to be the closest to the CCSD(T)/CBS (coupled clusters covering iterative single- and double-electron excitations and perturbative triple-electron excitations performed at the complete basis set limit) geometries among all the tested methods (e.g. MP3, SCS(MI)-MP2, MP2, M06-2X, and DFT-D method evaluated with the TPSS functional). The MP2.5 geometries for the tested complexes deviate from the references almost negligibly. Inclusion of the scaled third-order correlation energy results in a substantial improvement of the ability to accurately describe noncovalent interactions. The results shown here serve to support the notion that MP2.5 and MP2.X are reasonable alternative methods for benchmark calculations in cases where system size or (lack of) computational resources preclude the use of CCSD(T)/CBS computations. MP2.X allows for the use of smaller basis sets (i.e. 6-31G*) with results that are nearly identical to those of MP2.5 with larger basis sets, which dramatically decreases computation times and makes calculations on much larger systems possible.

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The structure and stabilization energies of benzene (and methylated benzenes)···X(2) (X=F, Cl, Br, N) complexes were investigated by performing CCSD(T)/complete basis set limit and density functional theory/symmetry-adapted perturbation theory (DFT-SAPT) calculations. The global minimum of the benzene···dihalogen complexes corresponds to the T-shaped structure, whereas that of benzene···dinitrogen corresponds to the sandwich one. The different binding motifs of these complexes arise from the different quadrupole moments of dihalogens and dinitrogen. The different sign of the quadrupole moments of these diatomics is explained based on the electrostatic potential (ESP). Whereas all dihalogens, including difluorine, possess a positive σ hole, such a positive area of the ESP is completely missing in the case of dinitrogen. Moreover, benzene···X(2) (X=Br, Cl) complexes are stronger than benzene···X(2) (X=F, N) complexes. When analyzing DFT-SAPT electrostatic, dispersion, induction, and δ(Hartree-Fock) energies, we recapitulate that the former complexes are stabilized mainly by dispersion energy, followed by electrostatic energy, whereas the latter complexes are stabilized mostly by the dispersion interaction. The charge-transfer energy of benzene···dibromine complexes, and surprisingly, also of methylated benzenes···dibromine complexes is only moderate, and thus, not responsible for their stabilization. Benzene···dichlorine and benzene···dibromine complexes can thus be characterized merely as complexes with a halogen bond rather than as charge-transfer complexes.

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The structure of the phenylacetylene-dimer has been elucidated using IR-UV double resonance spectroscopy in combination with high level ab initio calculations at the CCSD(T)/CBS level. The IR spectra in the acetylenic and the aromatic C-H stretching regions indicate that the two phenylacetylene moieties are in identical environments and very similar to the phenylacetylene monomer. Calculated stabilization energies and the free energies at the CCSD(T)/CBS level favor the formation of an anti-parallel π-stacked structure. The DFT-SAPT energy decomposition analysis points out that the anti-parallel π-stacked structure maximizes electrostatic as well as the dispersion components of energy. The observed IR spectra are consistent with the anti-parallel π-stacked structure.

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Weak, medium, and strong charge-transfer (CT) complexes containing various electron donors (C(2)H(4), C(2)H(2), NH(3), NMe(3), HCN, H(2)O) and acceptors (F(2), Cl(2), BH(3), SO(2)) were investigated at the CCSD(T)/complete basis set (CBS) limit. The nature of the stabilization for these CT complexes was evaluated on the basis of perturbative NBO calculations and DFT-SAPT/CBS calculations. The structure of all of the complexes was determined by the counterpoise-corrected gradient optimization performed at the MP2/cc-pVTZ level, and most of complexes possess a linear-like contact structure. The total stabilization energies lie between 1 and 55 kcal/mol and the strongest complexes contain BH(3) as an electron acceptor. When ordering the electron donors and electron acceptors on the basis of these energies, we obtain the same order as that based on the perturbative E2 charge-transfer energies, which provides evidence that the charge-transfer term is the dominant energy contribution. The CCSD(T) correction term, defined as the difference between the CCSD(T) and MP2 interaction energies, is mostly small, which allows the investigation of the CT complexes of this type at the "cheap" MP2/CBS level. In the case of weak and medium CT complexes (with stabilization energy smaller than about 15 kcal/mol), the dominant stabilization originates in the electrostatic term; the dispersion as well as induction and δ(HF) terms covering the CT energy contribution are, however, important as well. For strong CT complexes, induction energy is the second (after electrostatic) most important energy term. The role of the induction and δ(HF) terms is unique and characteristic for CT complexes. For all CT complexes, the CCSD(T)/CBS and DFT-SAPT/CBS stabilization energies are comparable, and surprisingly, it is true even for very strong CT complexes with stabilization energy close to 50 kcal/mol characteristic by substantial charge transfer (more than 0.3 e). It is thus possible to conclude that perturbative DFT-SAPT analysis is robust enough to be applied even for dative-like complexes with substantial charge transfer.

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The noncovalent interactions of heteroboranes with aromatic systems have only recently been acknowledged as a source of stabilization in supramolecular complexes. The physical basis of these interactions has been studied in several model complexes using advanced computational methods. The highly accurate CCSD(T)/complete basis set (CBS) value of the interaction energy for the model diborane···benzene complex in a stacking geometry exhibiting a B(2)H···π hydrogen bond was calculated to be -4.0 kcal·mol(-1). The DFT-SAPT/CBS approach, which is shown to reproduce the CCSD(T)/CBS data reliably asserted that the major stabilizing component was dispersion, followed by electrostatics. Furthermore, the effect of the benzene heteroatom- and exosubstitutions was studied and found to be small. Next, when aromatic molecules were changed to cyclic aliphatic ones, van der Waals complexes stabilized by the dispersion term only were formed. As the last step, interactions of two larger icosahedral borane cages with benzene were explored. The complex of the monoanionic CB(11)H(12)(-) exhibited two minima: the first stacked above the plane of the benzene ring with a C-H···π hydrogen bond and the second planar, in which the carborane cage bound to benzene via five B-H···H-C dihydrogen bonds. The DFT-SAPT/CBS calculations revealed that both of these binding motifs were stabilized by dispersion followed by electrostatic terms, with the planar complex being 1.4 kcal·mol(-1) more stable than the stacked one. The dianionic B(12)H(12)(2-) interacted with benzene only in the planar geometry, similarly as smaller anions do. The large stabilization energy of 11.0 kcal·mol(-1) was composed of dominant attractive dispersion and slightly smaller electrostatic and induction terms. In summary, the borane/carborane···aromatic interaction is varied both in the complex geometries and in the stabilizing energy components. The detailed insight derived from high-level quantum chemical computations can help us understand such important processes as host-guest complexation or carborane···biomolecule interactions.

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The structure of the binary complex between phenylacetylene and borane-trimethylamine has been elucidated using IR-UV double resonance spectroscopy in combination with high level ab initio calculations at the CCSD(T) level. Borane-trimethylamine interacts primarily through multiple C-H...pi interactions with the pi electron density of the benzene ring in phenylacetylene. CCSD(T) level calculations provide reliable estimates for the interaction energy and free energy, which are in accord with the experimental observations. The DFT-SAPT calculations point out that the dispersion interaction plays a major role in the formation of the experimentally observed complex, along with a sizable contribution from electrostatics.

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