A thorough benchmark of density functional methods for general main group thermochemistry, kinetics, and noncovalent interactions

A thorough energy benchmark study of various density functionals (DFs) is carried out with the new GMTKN30 database for general main group thermochemistry, kinetics and noncovalent interactions [Goerigk and Grimme, J. Chem. Theor. Comput., 2010, 6, 107; Goerigk and Grimme, J. Chem. Theor. Comput., 2011, 7, 291]. In total, 47 DFs are investigated: two LDAs, 14 GGAs, three meta-GGAs, 23 hybrids and five double-hybrids. Besides the double-hybrids, also other modern approaches, i.e., the M05 and M06 classes of functionals and range-separated hybrids, are tested. For almost all functionals, the new DFT-D3 correction is applied in order to consistently test the performance also for important noncovalent interactions; the parameters are taken from previous works or determined for the present study. Basis set and quadrature grid issues are also considered. The general aim of the study is to work out which functionals are generally well applicable and robust to describe the energies of molecules. In summary, we recommend on the GGA level the B97-D3 and revPBE-D3 functionals. The best meta-GGA is oTPSS-D3 although meta-GGAs represent in general no clear improvement compared to numerically simpler GGAs. Notably, the widely used B3LYP functional performs worse than the average of all tested hybrids and is also very sensitive to the application of dispersion corrections. We discourage its usage as a standard method without closer inspection of the results, as it still seems to be often done nowadays. Surprisingly, long-range corrected exchange functionals do in general not perform better than the corresponding standard hybrids. However, the ωB97X-D functional seems to be a promising method. The most robust hybrid is Zhao and Truhlar's PW6B95 functional in combination with DFT-D3. If higher accuracy is required, double-hybrids should be applied. The corresponding DSD-BLYP-D3 and PWPB95-D3 variants are the most accurate and robust functionals of the entire study. Additional calculations with MP2 and and its spin-scaled variants SCS-MP2, S2-MP2 and SOS-MP2 revealed that double-hybrids in general outperform those. Only SCS-MP2 can be recommended, particularly for reaction energies. We suggest its usage when a large self-interaction error is expected that prohibits usage of double-hybrids. Perdews' metaphoric picture of Jacob's Ladder for the classification of density functionals' performance could unbiasedly be confirmed with GMTKN30. We also show that there is no statistical correlation between a functional's accuracy for atomization energies and the performance for chemically more relevant reaction energies.     

Assessment of density functional methods for reaction energetics: Iridium‐catalyzed water oxidation as case study

We investigate basis set convergence for a series of density functional theory (DFT) functionals (both hybrid and nonhybrid) and compare to coupled‐cluster with single and double excitations and perturbative triples [CCSD(T)] benchmark calculations. The case studied is the energetics of the water oxidation reaction by an iridium‐oxo complex. Complexation energies for the reactants and products complexes as well as the transition state (TS) energy are considered. Contrary to the expectation of relatively weak basis set dependence for DFT, the basis set effects are large, for example, more than 10 kcal mol^?1 difference from converged basis for the activation energy with “small” basis sets (DZ/6‐31G** for Ir/other atoms, or SVP) and still more than 6 kcal mol^?1 for def2‐TZVPP/6‐31G**. Inclusion of the dispersion correction in DFT‐D3 schemes affects the energies of reactant complex (RC), TS, and product complex (PC) by almost the same amount; it significantly improves the complexation energy (the formation of RC), but has little effect on the activation energy with respect to RC. With converged basis, some pure GGAs (PBE‐D3, BP86‐D3) as well as the hybrid functional B3LYP‐D3 are very accurate compared to benchmark CCSD(T) calculations. © 2012 Wiley Periodicals, Inc.     

DFT,DLPNO-CCSD(T), and NEVPT2 benchmark study of the reaction between ferrocenium and trimethylphosphine

The reaction between ferrocenium and trimethylphosphine was studied using density functional theory (DFT), domain-based local pair natural orbital coupled cluster theory with single-, double-, and perturbative triple excitations (DLPNO-CCSD(T)), and N-electron valence state perturbation theory (NEVPT2). The accuracy of the DFT functionals decreases compared to the DLPNO-CCSD(T) level in the following order: M06-L > TPSS > M06, BLYP > PBE, PBE0, B3LYP > > PWPB95 > > DSD-BLYP. The roles of thermochemical, continuum solvation (SMD), and counterpoise corrections were evaluated. Grimme's D3 empirical dispersion correction is essential for all functionals studied except M06 and M06-L. The reliability of the frequency calculations performed directly within the SMD was confirmed. The systems showed no significant multireference character according to T₁ and T₂ diagnostics and the fractional occupation number (FOD) weighted electron density analysis. The multireference NEVPT2 calculations gave qualitatively valid conclusions about the reaction mechanism. However, a multireference approach is generally not recommended because it requires arbitrary chosen active spaces.     

Density functional theory study of trans-dioxo complexes of iron, ruthenium, and osmium with saturated amine ligands, trans-[M(O)2(NH3)2(NMeH2)2]2+ (M=Fe, Ru, Os), and detection of [Fe(qpy)(O)2]n+ (n=1, 2) by high-resolution ESI mass spectrometry

Density functional theory (DFT) calculations on trans-dioxo metal complexes containing saturated amine ligands, trans-[M(O)2(NH3)2(NMeH2)2]2+ (M=Fe, Ru, Os), were performed with different types of density functionals (DFs): 1) pure generalized gradient approximations (pure GGAs): PW91, BP86, and OLYP; 2) meta-GGAs: VSXC and HCTH407; and 3) hybrid DFs: B3LYP and PBE1PBE. With pure GGAs and meta-GGAs, a singlet d2 ground state for trans-[Fe(O)2(NH3)2(NMeH2)2]2+ was obtained, but a quintet ground state was predicted by the hybrid DFs B3LYP and PBE1PBE. The lowest transition energies in water were calculated to be at lambda approximately 509 and 515 nm in the respective ground-state geometries from PW91 and B3LYP calculations. The nature of this transition is dependent on the DFs used: a ligand-to-metal charge-transfer (LMCT) transition with PW91, but a pi(Fe-O)-->pi*(Fe-O) transition with B3LYP, in which pi and pi* are the bonding and antibonding combinations between the dpi(Fe) and ppi(O(2-)) orbitals. The FeVI/V reduction potential of trans-[Fe(O)2(NH3)2NMeH2)2]2+ was estimated to be +1.30 V versus NHE based on PW91 results. The [Fe(qpy)(O)2](n+) (qpy=2,2':6',2':6',2':6',2'-quinquepyridine; n=1 and 2) ions, tentatively assigned to dioxo iron(V) and dioxo iron(VI), respectively, were detected in the gas phase by high-resolution ESI-MS spectroscopy.     

How reliable is DFT in predicting relative energies of polycyclic aromatic hydrocarbon isomers? comparison of functionals from different rungs of jacob's ladder

Density functional theory (DFT) is the only quantum‐chemical avenue for calculating thermochemical/kinetic properties of large polycyclic aromatic hydrocarbons (PAHs) such as graphene nanoflakes. Using CCSD(T)/CBS PAH isomerization energies, we find that all generalized gradient approximation (GGA) and meta GGA DFT functionals have severe difficulties in describing isomerization energies in PAHs. The poor performance of these functionals is demonstrated by the following root‐mean‐square deviations (RMSDs) obtained for a database of C₁₄H₁₀ and C₁₈H₁₂ isomerization energies. The RMSDs for the GGAs range between 6.0 (BP86‐D3) and 23.0 (SOGGA11) and for the meta GGAs they range between 3.5 (MN12‐L) and 11.9 (τ‐HCTH) kJ mol⁻¹. These functionals (including the dispersion‐corrected methods) systematically and significantly underestimate the isomerization energies. A consequence of this behavior is that they all predict that chrysene (rather than triphenylene) is the most stable C₁₈H₁₂ isomer. A general improvement in performance is observed along the rungs of Jacob's Ladder; however, only a handful of functionals from rung four give good performance for PAH isomerization energies. These include functionals with high percentages (40–50%) of exact Hartree–Fock exchange such as the hybrid GGA SOGGA11‐X (RMSD = 1.7 kJ mol⁻¹) and the hybrid‐meta GGA BMK (RMSD = 1.3 kJ mol⁻¹). Alternatively, the inclusion of lower percentages (20–30%) of exact exchange in conjunction with an empirical dispersion correction results in good performance. For example, the hybrid GGA PBE0‐D3 attains an RMSD of 1.5 kJ mol⁻¹, and the hybrid‐meta GGAs PW6B95‐D3 and B1B95‐D3 result in RMSDs below 1 kJ mol⁻¹. © 2016 Wiley Periodicals, Inc.     

Accurate reaction barrier heights of pericyclic reactions: Surprisingly large deviations for the CBS‐QB3 composite method and their consequences in DFT benchmark studies

Accurate barrier heights are obtained for the 26 pericyclic reactions in the BHPERI dataset by means of the high‐level Wn‐F12 thermochemical protocols. Very often, the complete basis set (CBS)‐type composite methods are used in similar situations, but herein it is shown that they in fact result in surprisingly large errors with root mean square deviations (RMSDs) of about 2.5 kcal mol^?1. In comparison, other composite methods, particularly G4‐type and estimated coupled cluster with singles, doubles, and quasiperturbative triple excitations [CCSD(T)/CBS] approaches, show deviations well below the chemical‐accuracy threshold of 1 kcal mol^?1. With the exception of SCS‐MP2 and the herein newly introduced MP3.5 approach, all other tested Møller‐Plesset perturbative procedures give poor performance with RMSDs of up to 8.0 kcal mol^?1. The finding that CBS‐type methods fail for barrier heights of these reactions is unexpected and it is particularly troublesome given that they are often used to obtain reference values for benchmark studies. Significant differences are identified in the interpretation and final ranking of density functional theory (DFT) methods when using the original CBS‐QB3 rather than the new Wn‐F12 reference values for BHPERI. In particular, it is observed that the more accurate Wn‐F12 benchmark results in lower statistical errors for those methods that are generally considered to be robust and accurate. Two examples are the PW6B95‐D3(BJ) hybrid‐meta‐general‐gradient approximation and the PWPB95‐D3(BJ) double‐hybrid functionals, which result in the lowest RMSDs of the entire DFT study (1.3 and 1.0 kcal mol^?1, respectively). These results indicate that CBS‐QB3 should be applied with caution in computational modeling and benchmark studies involving related systems. © 2015 Wiley Periodicals, Inc.     

Analysis of Kojic Acid Derivatives as Competitive Inhibitors of Tyrosinase: A Molecular Modeling Approach

Tyrosinases belong to the functional copper-containing proteins family, and their structure contains two copper atoms, in the active site, which are coordinated by three histidine residues. The biosynthesis of melanin in melanocytes has two stages depending on the actions of the natural substrates L-DOPA and L-tyrosine. The dysregulation of tyrosinase is involved in skin cancer initiation. In the present study, using molecular modeling tools, we analyzed the inhibition activity of tyrosinase activity using kojic acid (KA) derivatives designed from aromatic aldehydes and malononitrile. All derivatives showed conformational affinity to the enzyme active site, and a favorable distance to chelate the copper ion, which is essential for enzyme function. Molecular dynamics simulations revealed that the derivatives formed promising complexes, presenting stable conformations with deviations between 0.2 and 0.35 Å. In addition, the investigated KA derivatives showed favorable binding free energies. The most stable KA derivatives showed the following binding free energies: −17.65 kcal mol⁻¹ (D6), −18.07 kcal mol⁻¹ (D2), −18.13 (D5) kcal mol⁻¹, and −10.31 kcal mol⁻¹ (D4). Our results suggest that these derivatives could be potent competitive inhibitors of the natural substrates of L-DOPA (−12.84 kcal mol⁻¹) and L-tyrosine (−9.04 kcal mol⁻¹) in melanogenesis.     

Benchmarking the Fluxional Processes of Organometallic Piano-Stool Complexes

The correlation consistent Composite Approach for transition metals (ccCA-TM) and density functional theory (DFT) computations have been applied to investigate the fluxional mechanisms of cyclooctatetraene tricarbonyl chromium ((COT)Cr(CO)₃) and 1,3,5,7-tetramethylcyclooctatetraene tricarbonyl chromium, molybdenum, and tungsten ((TMCOT)M(CO)₃ (M = Cr, Mo, and W)) complexes. The geometries of (COT)Cr(CO)₃ were fully characterized with the PBEPBE, PBE0, B3LYP, and B97-1 functionals with various basis set/ECP combinations, while all investigated (TMCOT)M(CO)₃ complexes were fully characterized with the PBEPBE, PBE0, and B3LYP methods. The energetics of the fluxional dynamics of (COT)Cr(CO)₃ were examined using the correlation consistent Composite Approach for transition metals (ccCA-TM) to provide reliable energy benchmarks for corresponding DFT results. The PBE0/BS1 results are in semiquantitative agreement with the ccCA-TM results. Various transition states were identified for the fluxional processes of (COT)Cr(CO)₃. The PBEPBE/BS1 energetics indicate that the 1,2-shift is the lowest energy fluxional process, while the B3LYP/BS1 energetics (where BS1 = H, C, O: 6-31G(d′); M: mod-LANL2DZ(f)-ECP) indicate the 1,3-shift having a lower electronic energy of activation than the 1,2-shift by 2.9 kcal mol⁻¹. Notably, PBE0/BS1 describes the (CO)₃ rotation to be the lowest energy process, followed by the 1,3-shift. Six transition states have been identified in the fluxional processes of each of the (TMCOT)M(CO)₃ complexes (except for (TMCOT)W(CO)₃), two of which are 1,2-shift transition states. The lowest-energy fluxional process of each (TMCOT)M(CO)₃ complex (computed with the PBE0 functional) has a ΔG^‡ of 12.6, 12.8, and 13.2 kcal mol⁻¹ for Cr, Mo, and W complexes, respectively. Good agreement was observed between the experimental and computed ¹H-NMR and ¹³C-NMR chemical shifts for (TMCOT)Cr(CO)₃ and (TMCOT)Mo(CO)₃ at three different temperature regimes, with coalescence of chemically equivalent groups at higher temperatures.     

Harmonic vibrational frequencies: scale factors for pure, hybrid, hybrid meta, and double-hybrid functionals in conjunction with correlation consistent basis sets

Scale factors for (a) low (<1000 cm(-1)) and high harmonic vibrational frequencies, (b) thermal contributions to enthalpy and entropy, and (c) zero-point vibrational energies have been determined for five hybrid functionals (B3P86, B3PW91, PBE1PBE, BH&HLYP, MPW1K), five pure functionals (BLYP, BPW91, PBEPBE, HCTH93, and BP86), four hybrid meta functionals (M05, M05-2X, M06, and M06-2X) and one double-hybrid functional (B2GP-PLYP) in combination with the correlation consistent basis sets [cc-pVnZ and aug-cc-pVnZ, n = D(2),T(3),Q(4)]. Calculations for vibrational frequencies were carried out on 41 organic molecules and an additional set of 22 small molecules was used for the zero-point vibrational energy scale factors. Before scaling, approximately 25% of the calculated frequencies were within 3% of experimental frequencies. Upon application of the derived scale factors, nearly 90% of the calculated frequencies deviated less than 3% from the experimental frequencies for all of the functionals when the augmented correlation consistent basis sets were used.     

In Silico Studies of Some Isoflavonoids as Potential Candidates against COVID-19 Targeting Human ACE2 (hACE2) and Viral Main Protease (Mpro)

The Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) caused the “COVID-19” disease that has been declared by WHO as a global emergency. The pandemic, which emerged in China and widespread all over the world, has no specific treatment till now. The reported antiviral activities of isoflavonoids encouraged us to find out its in silico anti-SARS-CoV-2 activity. In this work, molecular docking studies were carried out to investigate the interaction of fifty-nine isoflavonoids against hACE2 and viral M^pro. Several other in silico studies including physicochemical properties, ADMET and toxicity have been preceded. The results revealed that the examined isoflavonoids bound perfectly the hACE-2 with free binding energies ranging from −24.02 to −39.33 kcal mol⁻¹, compared to the co-crystallized ligand (−21.39 kcal mol^–1). Furthermore, such compounds bound the M^pro with unique binding modes showing free binding energies ranging from −32.19 to −50.79 kcal mol^–1, comparing to the co-crystallized ligand (binding energy = −62.84 kcal mol^–1). Compounds 33 and 56 showed the most acceptable affinities against hACE2. Compounds 30 and 53 showed the best docking results against M^pro. In silico ADMET studies suggest that most compounds possess drug-likeness properties.     

On the DFT Ground State of Crystalline Bromine and Iodine

We report on an erroneous ground state within common density functional theory (DFT) methods for the solid elements bromine and iodine. Phonon computations at the GGA level for both molecular crystals yield imaginary vibrational modes, erroneously indicating dynamic instability—that fact alone could easily pass as a computational artefact, but these imaginary modes lead to energetically more favorable and dynamically stable structures, made up of infinite monoatomic chains. In contrast, meta‐GGA and hybrid functionals yield the correct energetic order for bromine, while for iodine, most global hybrids do not improve the GGA result significantly. The qualitatively correct answer, in both cases, is given by the long‐range corrected hybrid LC‐ωPBE, the Minnesota functionals M06L and M06, and by periodic Hartree–Fock and MP2 theory. This poor performance of economic DFT functionals should be kept in mind, for example, during global structure optimizations of systems with significant contributions from halogen bonds.     

Spin‐component‐scaled double hybrids: An extensive search for the best fifth‐rung functionals blending DFT and perturbation theory

Following up on an earlier preliminary communication (Kozuch and Martin, Phys. Chem. Chem. Phys. 2011, 13 , 20104), we report here in detail on an extensive search for the most accurate spin‐component‐scaled double hybrid functionals [of which conventional double hybrids (DHs) are a special case]. Such fifth‐rung functionals approach the performance of composite ab initio methods such as G3 theory at a fraction of their computational cost, and with analytical derivatives available. In this article, we provide a critical analysis of the variables and components that maximize the accuracy of DHs. These include the selection of the exchange and correlation functionals, the coefficients of each component [density functional theory (DFT), exact exchange, and perturbative correlation in both the same spin and opposite spin terms], and the addition of an ad‐hoc dispersion correction; we have termed these parametrizations “DSD‐DFT” (Dispersion corrected, Spin‐component scaled, Double‐hybrid DFT). Somewhat surprisingly, the quality of DSD‐DFT is only mildly dependent on the underlying DFT exchange and correlation components, with even DSD‐LDA yielding respectable performance. Simple, nonempirical GGAs appear to work best, whereas meta‐GGAs offer no advantage (with the notable exception of B95c). The best correlation components appear to be, in that order, B95c, P86, and PBEc, while essentially any good GGA exchange yields nearly identical results. On further validation with a wider variety of thermochemical, weak interaction, kinetic, and spectroscopic benchmarks, we find that the best functionals are, roughly in that order, DSD‐PBEhB95, DSD‐PBEP86, DSD‐PBEPW91, and DSD‐PBEPBE. In addition, DSD‐PBEP86 and DSD‐PBEPBE can be used without source code modifications in a wider variety of electronic structure codes. Sample job decks for several commonly used such codes are supplied as electronic Supporting Information. Copyright © 2013 Wiley Periodicals, Inc.     

Energy landscapes of nucleophilic substitution reactions: a comparison of density functional theory and coupled cluster methods

We have carried out a detailed evaluation of the performance of all classes of density functional theory (DFT) for describing the potential energy surface (PES) of a wide range of nucleophilic substitution (SN2) reactions involving, amongst others, nucleophilic attack at carbon, nitrogen, silicon, and sulfur. In particular, we investigate the ability of the local density approximation (LDA), generalized gradient approximation (GGA), meta-GGA as well as hybrid DFT to reproduce high-level coupled cluster (CCSD(T)) benchmarks that are close to the basis set limit. The most accurate GGA, meta-GGA, and hybrid functionals yield mean absolute deviations of about 2 kcal/mol relative to the coupled cluster data, for reactant complexation, central barriers, overall barriers as well as reaction energies. For the three nonlocal DFT classes, the best functionals are found to be OPBE (GGA), OLAP3 (meta-GGA), and mPBE0KCIS (hybrid DFT). The popular B3LYP functional is not bad but performs significantly worse than the best GGA functionals. Furthermore, we have compared the geometries from several density functionals with the reference CCSD(T) data. The same GGA functionals that perform best for the energies (OPBE, OLYP), also perform best for the geometries with average absolute deviations in bond lengths of 0.06 A and 0.6 degrees, even better than the best meta-GGA and hybrid functionals. In view of the reduced computational effort of GGAs with respect to meta-GGAs and hybrid functionals, let alone coupled cluster, we recommend the use of accurate GGAs such as OPBE or OLYP for the study of SN2 reactions.     

Performance of Density Functional Theory for Transition Metal Oxygen Bonds

The accuracy of density functional theory (DFT) limits predictions in theoretical catalysis, and strong chemical bonds between transition metals and oxygen pose a particular challenge. We benchmarked 30 diverse density functionals against the bond dissociation enthalpies (BDE) of the 30 MO and 30 MO⁺ diatomic systems of all the 3d, 4d, and 5d metals, to test universality across the d-block as required in comparative studies. Seven functionals, B98, B97-1, B3P86, B2PLYP, TPSSh, B3LYP, and B97-2, display mean absolute errors (MAE) <30 kJ/mol. In contrast, many commonly used functionals such as PBE and RPBE overestimate M−O bonding by +30 kJ/mol and display MAEs from 48–76 kJ/mol. RPBE and OPBE reduce the over-binding of PBE but remain very inaccurate. We identify a linear relationship (p-value 7.6 ⋅ 10⁻⁵) between the precision and accuracy of DFT, i. e. inaccurate functionals tend to produce larger, unpredictable random errors. Some functionals commonly deviate from this relationship: Thus, M06-2X is very precise but not very accurate, whereas B3LYP* and MN15-L are more accurate but less precise than M06-2X. The best-performing hybrids have 10–30 % HF exchange, but this can be relieved by double hybrids (B2PLYP). Most functionals describe trends well, but errors comparing 5d to 4d/3d are ∼10 kJ/mol larger than group-wise errors, due to uncertainties in the spin-orbit coupling corrections for effective core potentials, affecting e. g. Pt/Pd or Au/Ag comparisons.     

Aphrodisiac Performance of Bioactive Compounds from Mimosa pudica Linn.: In Silico Molecular Docking and Dynamics Simulation Approach

Plants and their derived molecules have been traditionally used to manage numerous pathological complications, including male erectile dysfunction (ED). Mimosa pudica Linn. commonly referred to as the touch-me-not plant, and its extract are important sources of new lead molecules in drug discovery research. The main goal of this study was to predict highly effective molecules from M. pudica Linn. for reaching and maintaining penile erection before and during sexual intercourse through in silico molecular docking and dynamics simulation tools. A total of 28 bioactive molecules were identified from this target plant through public repositories, and their chemical structures were drawn using Chemsketch software. Graph theoretical network principles were applied to identify the ideal target (phosphodiesterase type 5) and rebuild the network to visualize the responsible signaling genes, proteins, and enzymes. The 28 identified bioactive molecules were docked against the phosphodiesterase type 5 (PDE5) enzyme and compared with the standard PDE5 inhibitor (sildenafil). Pharmacokinetics (ADME), toxicity, and several physicochemical properties of bioactive molecules were assessed to confirm their drug-likeness property. Molecular dynamics (MD) simulation modeling was performed to investigate the stability of PDE5–ligand complexes. Four bioactive molecules (Bufadienolide (−12.30 kcal mol⁻¹), Stigmasterol (−11.40 kcal mol⁻¹), Isovitexin (−11.20 kcal mol⁻¹), and Apigetrin (−11.20 kcal mol⁻¹)) showed the top binding affinities with the PDE5 enzyme, much more powerful than the standard PDE5 inhibitor (−9.80 kcal mol⁻¹). The four top binding bioactive molecules were further validated for a stable binding affinity with the PDE5 enzyme and conformation during the MD simulation period as compared to the apoprotein and standard PDE5 inhibitor complexes. Further, the four top binding bioactive molecules demonstrated significant drug-likeness characteristics with lower toxicity profiles. According to the findings, the four top binding molecules may be used as potent and safe PDE5 inhibitors and could potentially be used in the treatment of ED.     

Experimental and quantum-chemical study of complexation of carbene analogs with dinitrogen. Direct IR-spectroscopic observation of Cl2Si·N2 complexes in low-temperature argon-nitrogen matrices

Interaction of dichlorosilylene with dinitrogen in mixed Ar—N₂ matrices at 9 - 10 K was studied by IR spectroscopy. A donor-acceptor complex Cl₂Si·N₂ was found and characterized by six bands of symmetric (at 511.2, 508.9, and 506.5 cm^–1) and antisymmetric (at 500.1, 496.9, and 495.1 cm^–1) stretching vibrations of Si—Cl bonds in the most abundant isotopomers. Two bands at 498.7 and 493.5 cm^–1 observed in mixed matrices were tentatively assigned to Cl₂Si·(N₂)₂ complex. Several stretching vibration bands of minor isotopomers of SiCl₂ were detected for the first time in argon matrices. Assignment has been done for the isotopic structure of SiCl₂ associates with dinitrogen observed in N₂ matrices. Dimerization of SiCl₂ and its complexation with one and two N₂ molecules were studied by quantum-chemical DFT calculations (PBE and B3LYP functionals). The structures, energies, and vibrational frequencies of the Cl₂Si·N₂ and Cl₂Si·(N₂)₂ complexes and the Si₂Cl₄ dimer were determined. The energies of SiCl₂ complexation with one and two N₂ molecules obtained from PBE and B3LYP calculations are 0.3 and 0.6 kcal mol^–1, respectively. More accurate G2(MP2,SVP) calculations using the B3LYP geometries have predicted a higher stability of the Cl₂Si·N₂ complex (1.2 kcal mol^–1). The calculated and experimental vibrational frequencies of reagents and complexes are in good agreement. A correlation has been established between the PBE calculated energies of complexation of EHal₂ (E = Si, Ge, Sn, Pb) with N₂ and the experimentally observed shifts of E—Hal stretching vibrations in EHal₂ upon complexation. The strength of the complexes with N₂ increases on going from dihalosilylenes to dihaloplumbylenes.     

Reactions between germylenes (silylenes) and phosphaalkenes: an experimental and theoretical study. Preparation of the first representative of germaphosphacyclopropanes

Reactions of a number of germylenes and dimethylsilylene with a phosphaalkene, 2,2-bis(trimethylsilyl)-1-phenyl-1-phosphaethene (1), were studied. The reaction of short-lived dimethylgermylene with 1 produced a phosphagermirane 3 (the first representative of a new class of heterocyclic compounds). Compound 3 was characterized in solution by ¹H, ¹³C, ³¹P, and ²⁹Si NMR spectroscopy. Subsequent reaction of 3 with dimethylgermylene results in 2,2,3,3-tetramethyl-4,4-bis(trimethylsilyl)-1-phenyl-2,3-digerma-1-phosphacyclobutane 4, which has not been reported so far. In order to rationalize different reactivities of germylenes towards alkenes and phosphaalkenes, the addition products of GeH₂ to ethylene and phosphaethene (HP=CH₂) were studied using the G2 computational scheme and DFT PBE technique. The adducts of GeMe₂ (GeCl₂) with HP=CH₂ and of GeMe₂ with PhP=C(SiH₃)₂ were also calculated by the DFT PBE method. According to calculations, the exothermicity, DE, of cycloaddition of GeH₂ and GeMe₂ to the phosphaalkenes HP=CH₂ and PhP=C(SiH₃)₂ (43.5—39.7 kcal mol^–1) is nearly twice as high as the exothermicity of cycloaddition of these germylenes to ethylene. In addition to the minimum corresponding to the three-membered cycle, a number of minima corresponding to quite stable donor-acceptor complexes in which the Ge atom is coordinated by the lone electron pair of the P atom in the phosphaalkene molecule were located on the potential energy surface of the germylene—phosphaalkene system. The complexation energy of the complex of GeH₂ (GeMe₂) with phosphaethene is 25.0 (16.9) kcal mol^–1. For GeCl₂, the exothermicity of cycloaddition to HP=CH₂ decreases to 7.6 kcal mol^–1 and the complexation energy decreases to 8.2 kcal mol^–1.