A grid-based variational method was proposed and applied to the ground state energies of atoms from the first to the third period of the periodic table. The nonuniform grid in the radial coordinate was defined by a q-exponential sequence. Some unusual properties between the optimum q-parameters and the electronic energies or atomic numbers are described. The behavior of the electronic energy, with respect to the q-parameter, yields near Hartree-Fock accuracy with a relatively small number of integration points. A simple relationship between the optimum q-parameters and the atomic numbers was found, which allowed the determination of the optimum q-parameters for atoms of the same period from two results. The remarkable results provide a simple alternative route to reach accurate results. The consistent results also suggest that this is not a random or accidental effect, but some optimum condition achieved by using a q-exponential mesh grid.
Density functional theory (B3LYP, B3LYP-D2 and wB97XD functionals) was used in finite models of zigzag carbon nanotubes (CNT), (n,0)×k with n?=?6–9 and k?=?2–4, to systematically investigate the effects of size on their structural and electronic properties. We found that the ratio between the length (Lt) and the diameter (dt) of the pristine CNT has to be larger than 2, i.e., Lt/dt?>?2, in order to provide the observed experimental trends of C=C bond distances, as well as to maintain the atomic charges nearly constant and zero around the center of the tube. Therefore, the concepts of useful length and volume were developed and tested for the encapsulation process of HCN and C2H2 into CNTs. The energies involved in these processes, as well as the changes in molecular structure and electronic properties of the dopants and the CNTs are discussed and rationalized by the amount of charge transferred between dopant and CNT.
Density functional theory (DFT) was used to study the cobalt(I)-catalyzed enantioselective intramolecular hydroacylation of ketones and alkenes. All intermediates and transition states were fully optimized at the M06/6-31G(d,p) level (LANL2DZ(f) for Co). The results demonstrated that the ketone and alkene present different reactivities in the enantioselective hydroacylation. In ketone hydroacylation catalyzed by the cobalt(I)–(R,R)-Ph-BPE complex, reaction channel “a” to (R)-phthalide was more favorable than channel “b” to (S)-phthalide. Hydrogen migration was both the rate-determining and chirality-limiting step, and this step was endothermic. In alkene hydroacylation catalyzed by the cobalt(I)–(R,R)-BDPP complex, reaction channel “c” leading to the formation of (S)-indanone was the most favorable, both thermodynamically and kinetically. Reductive elimination was the rate-determining step, but the chirality-limiting step was hydrogen migration, which occurred easily. The results also indicated that the alkene hydroacylation leading to (S)-indanone formation was more energetically favorable than the ketone hydroacylation that gave (R)-phthalide, both thermodynamically and kinetically.
Graphical abstract A DFT study demonstrated that the ketone and alkene in the cobalt(I)-catalyzed enantioselective intramolecular hydroacylation showed different reactivities
The present study reports the geometries, electronic structures, growth behavior, and stabilities of neutral and ionized copper-doped germanium clusters containing 1–20 Ge atoms within the framework of linear combination of atomic orbitals density functional theory (DFT) under the spin-polarized generalized gradient approximation. It was found that Cu-capped Gen (or Cu-substituted Gen+1) and Cu-encapsulated Gen clusters mostly occur in the ground state at a particular cluster size (n). In order to explain the relative stabilities of the ground-state clusters, parameters such as the average binding energy per atom (BE), the embedding energy (EE), and the fragmentation energy (FE) of the clusters were calculated, and the resulting values are discussed. To explain the chemical stabilities of the clusters, parameters such as the energy gap between the highest occupied and the lowest unoccupied molecular orbitals (the HOMO–LUMO gap), the ionization energy (IP), the electron affinity (EA), the chemical potential (μ), the chemical hardness (η), and the polarizability were calculated, and the resulting values are also discussed. Natural atomic orbital (NAO) and natural bond orbital (NBO) analyses were also used to determine the electron-counting rule that should be applied to the most stable Ge10Cu cluster. Finally, the relevance of the calculated results to the design of Ge-based superatoms is discussed.
Figure Contributions of the valance orbitals of the Ge and Cu atom(s) to the HOMO of the ground-state icosahedral Ge10Cu cluster obtained from NBO analysis. The numbers below the clusters represent the occupancies of the HOMO orbitals
Multilayer-shaped compression and slide models were employed to investigate the complex sensitive mechanisms of cocrystal explosives in response to external mechanical stimuli. Here, density functional theory (DFT) calculations implementing the generalized gradient approximation (GGA) of Perdew-Burke-Ernzerhof (PBE) with the Tkatchenko-Scheffler (TS) dispersion correction were applied to a series of cocrystal explosives: diacetone diperoxide (DADP)/1,3,5-trichloro-2,4,6-trinitrobenzene (TCTNB), DADP/1,3,5-tribromo-2,4,6-trinitrobenzene (TBTNB) and DADP/1,3,5-triiodo-2,4,6-trinitrobenzene (TITNB). The results show that the GGA-PBE-TS method is suitable for calculating these cocrystal systems. Compression and slide models illustrate well the sensitive mechanism of layer-shaped cocrystals of DADP/TCTNB and DADP/TITNB, in accordance with the results from electrostatic potentials and free space per molecule in cocrystal lattice analyses. DADP/TCTNB and DADP/TBTNB prefer sliding along a diagonal direction on the a?c face and generating strong intermolecular repulsions, compared to DADP/TITNB, which slides parallel to the b?c face. The impact sensitivity of DADP/TBTNB is predicted to be the same as that of DADP/TCTNB, and the impact sensitivity of DADP/TBTNB may be slightly more insensitive than that of DADP and much more sensitive than that of TBTNB.
Since the thermal stabilities of ionic liquids (ILs) are of significance for their application, an amine-functionalized IL 1,2-dimethyl-(3-aminoethyl) imidazolium tetrafluoroborate [aEMMIM][BF4] was chosen to study thermal decomposition mechanisms via the methods of FT-IR, 1H NMR, TGA, TGA-MS and density functional theory (DFT) calculations. Theoretical and experimental results indicated that amine-functionalization reduces the thermal stability of [aEMMIM][BF4] compared to its non-functionalized counterpart. Moreover, we found that [aEMMIM][BF4] follows a unimolecular nucleophilic substitution (SN1) decomposition (98.8 %), whereas the bimolecular nucleophilic substitution (SN2) decomposition (1.2 %) is unfavorable. The SN1 and SN2 reactions were fully optimized at B3LYP/6-311++G(d,p) level, and the energies of reactant (R), intermediates (IM), transition state (TS) and product (P) were obtained and analyzed by reaction mechanism. The energy of the intermediate is higher than that of the reactants by 18.92 kJ mol?1, and the energy of the TS is higher than that of the IM by 155.23 kJ mol?1. This result indicates that the IM are also more stable than the P2 product, thus the reaction is endothermic. The chemical nature of the covalent and hydrogen bonds was analyzed by vibrational modes analysis (VMA), nature bond orbital (NBO) and the theory of atoms in molecules (AIM).
Graphical Abstract Proposed thermal decomposition of [aEMMIM][BF4] via unimolecular ( SN1) and bimolecular( SN2) nucleophilic substitution mechanisms. The electrostatic potential surface (ESP) of the transition state illustrates that hydrogen bonds are generated when [BF4]? is close to [aEMMIM]+, and SN1 decomposition is much favorable than SN2 decomposition.
We present a theoretical study on the detailed mechanism and kinetics of the H+HCN →H+HNC process. The potential energy surface was calculated at the complete basis set quantum chemical method, CBS-QB3. The vibrational frequencies and geometries for four isomers (H2CN, cis-HCNH, trans-HCNH, CNH2), and seven saddle points (TSn where n = 1 ? 7) are very important and must be considered during the process of formation of the HNC in the reaction were calculated at the B3LYP/6-311G(2d,d,p) level, within CBS-QB3 method. Three different pathways (PW1, PW2, and PW3) were analyzed and the results from the potential energy surface calculations were used to solve the master equation. The results were employed to calculate the thermal rate constant and pathways branching ratio of the title reaction over the temperature range of 300 up to 3000 K. The rate constants for reaction H + HCN → H + HNC were fitted by the modified Arrhenius expressions. Our calculations indicate that the formation of the HNC preferentially occurs via formation of cis–HCNH, the fitted expression is kPW2(T) = 9.98 × 10?22T2.41 exp(?7.62 kcal.mol?1/RT) while the predicted overall rate constant kOverall(T) = 9.45 × 10?21T2.15 exp(?8.56 kcal.mol?1/RT) in cm3 molecule?1s?1.
Graphical Abstract (a) Potential energy surface, (b) thermal rate constants as a function of temperature and (c) the branching ratios (%) of PW1, PW2, PW3 pathways involved in rm H + HCN → H + HNC process.
Fused hexaphyrins have many physical and chemical properties and can coordinate transition metal ions. In this study, we investigated the geometric structure, charge decomposition analysis (CDA), spin density, frontier molecular orbital (FMO) compositions and absorption spectra of four oxygen doubly N-confused hexaphyrin (1.1.1.1.1.1) (ONCP) complexes with the metal ions Co(II), Ni(II), Cu(II) and Zn(II) (designated ONCP-d-Co, ONCP-d-Ni, ONCP-d-Cu and ONCP-d-Zn). Based on their energies, geometric structures, FMO characteristics and comparison to experiments, ONCP-d-Co and ONCP-d-Cu have the mix-states of the triplet state and broken-symmetry state (antiferromagnetic state) rather than the spin singlet of a closed shell as previously reported. Moreover, based on analyses of the spin density and spin population of the spin triplet ONCP-d-Co and ONCP-d-Cu complexes, the charge transfer in ONCP-d-Cu is greater than that in ONCP-d-Co because the spin density in ONCP-d-Cu is concentrated not only on the Cu ion but also on the ONCP ligand. Thus, the CDA value for ONCP-d-Cu is larger. Finally, through comparative analysis of the FMO compositions and absorption spectra, the complexes and ligand are shown to have very similar absorption spectra with characteristics that arise mainly from π?→?π* transitions both in the B-band and the Q-band, which is due to the FMO compositions being dominated by the highly delocalized conjugated system, rather than by the metal ions. The absorption maxima of the Q-band are ONCP-d-Co (1020 nm)?>?ONCP-d-Zn (1012 nm)?>?ONCP-d-Ni (997 nm)?>?ONCP-d-Cu (988 nm), which is inversely proportional to the energy gap in their FMOs.
Graphical Abstract The present work investigates the geometric structure, charge decomposition analysis (CDA), spin density, frontier molecular orbital (FMO) compositions and absorption spectra of four oxygen doubly N-confused hexaphyrin (1.1.1.1.1.1) (ONCP) complexes with the metal ions Co(II), Ni(II), Cu(II) and Zn(II) (designated ONCP-d-Co, ONCP-d-Ni, ONCP-d-Cu and ONCP-d-Zn). Based on their energies, geometric structures, FMO characteristics and comparison to experiments, ONCP-d-Co and ONCP-d-Cu have the mix-state of the triplet state and broken-symmetry state (antiferromagnetic state) rather than the spin singlet of a close shell as were previously reported. Meanwhile, ONCP-d-Ni and ONCP-d-Zn show spin singlet structure. The calculated CDA shows the following order: ONCP-d-Cu (1.487)?>?ONCP-d-Ni (1.255)?>?ONCP-d-Co (1.211)?>?ONCP-d-Zn (1.201). Through comparisons of spin density and spin populations of ONCP-d-Co and ONCP-d-Cu, charge transfer between Cu and ligand ONCP is greater than that of Co and ONCP, which makes the CDA value of ONCP-d-Cu obviously larger than that of the other complexes
Density functional theory and its time-dependent extension (DFT, TDDFT) were employed to establish the feasibility of using a series of 4,4-difluoro-4-bora-3a,4a-diaza-s-indacenes (BODIPYs) in photodynamic therapy. Their absorption electronic spectra, singlet–triplet energy gaps, and spin–orbit matrix elements were computed and are discussed here. The effects of bromine substitution on the photophysical properties of BODIPY were elucidated. The investigated compounds were found to possess different excited triplet states that lie below the energy of the bright excited singlet state (S1 or S2), depending on the positions occupied by the bromine atoms. The computed spin–orbit matrix elements for the radiationless intersystem crossing Sn?→ ?Tm and the relative singlet–triplet energy gaps allowed the prediction of plausible nonradiative decay pathways for the production of singlet excited molecular oxygen, the key cytotoxic agent in photodynamic therapy.
Graphical Abstract The photophysical properties affected by the presence of bromine atoms in different positions of a BODIPY core have been here elucidated. In particular it has been found that SOC values strongly depend on the position of heavy atoms into the BODIPY core, suggesting positions 1 and 7 as the best ones to enhance the ISC kinetics
The reaction mechanisms and rates for the H abstraction reactions between CH3SS and CN radicals in the gas phase were investigated with density functional theory (DFT) methods. The geometries, harmonic vibrational frequencies, and energies of all stationary points were obtained at B3PW91/6-311G(d,p) level of theory. Relationships between the reactants, intermediates, transition states and products were confirmed, with the frequency and the intrinsic reaction coordinate (IRC) analysis at the same theoretical level. High accurate energy information was provided by the G3(MP2) method combined with the standard statistical thermodynamics. Gibbs free energies at 298.15 K for all of the reaction steps were reported, and were used to describe the profile diagrams of the potential energy surface. The rate constants were evaluated with both the classical transition state theory and the canonical variational transition state theory, in which the small-curvature tunneling correction was included. A total number of 9 intermediates (IMs) and 17 transition states (TSs) were obtained. It is shown that IM1 is the most stable intermediate by the largest energy release, and the channel of CH3SS?+?CN?→?IM3?→?TS10?→?P1(CH2SS?+?HCN) is the dominant reaction with the lowest energy barrier of 144.7 kJ mol?1. The fitted Arrhenius expressions of the calculated CVT/SCT rate constants for the rate-determining step of the favorable channel is k =7.73?×?106? T1.40exp(?14,423.8/T) s?1 in the temperature range of 200–2000 K. The apparent activation energy Ea(app.) for the main channel is ?102.5 kJ mol?1, which is comparable with the G3(MP2) energy barrier of ?91.8 kJ mol?1 of TS10 (relative to the reactants). 相似文献
The effect of alkali metal oxides MnO (M?=?Li, Na, K; n?=?2, 3, 4) on the geometric, electronic, and linear and nonlinear optical properties of the Mg12O12 nanocage was investigated by density-functional-based methods. According to the computational results, these alkali metal oxides are adsorbed on the Mg12O12 nanocage because this adsorption reduces its energy gap. The static first hyperpolarizability (β0) of the nanocage is dramatically increased in the presence of the alkali metal oxides, with the greatest increase seen in the presence of the superalkalis (i.e., M3O; M?=?Li, Na, and K). The highest first hyperpolarizability (β0?≈?600,000 a.u.) was calculated for K3O@Mg12O12, which was considerably more than that for Mg12O12. The thermodynamic properties and relative stabilities of these inorganic compounds are discussed.
Recently, a series of xanthone analogues has been identified as α-glucosidase inhibitors. To provide deeper insight into the three-dimensional (3D) structural requirements for the activities of these molecules, CoMFA and CoMSIA approaches were employed on 54 xanthones to construct 3D-QSAR models. Their bioactive conformations were first investigated by docking studies and optimized by subsequent molecular dynamics (MD) simulations using the homology modeled structure of the target protein. Based on the docking/MD-determined conformers, 3D-QSAR studies generated several significant models in terms of 47 molecules as the training set. The best model (CoMSIA-SHA) yielded q2 of 0.713, r2 of 0.967 and F of 140.250. The robustness of the model was further externally confirmed by a test set of the remaining molecules (q2 = 0.793, r2 = 0.902, and k = 0.905). Contour maps provided much information for future design and optimization of new compounds with high inhibitory activities towards α-glucosidase.
The absorption and emission spectra of dichlorvos and the dichlorvos-MAA complex in methanol, water, and chloroform in the molecularly imprinted recognition were investigated systematically. The M06-2X results revealed that: 1) the hydroxyl groups in polar solvents such as methanol and water may markedly influence the weak interactions, and then alter the adsorption and emission spectra; 2) the electronic excitation in absorption spectra of dichlorvos is dominated by the configuration HOMO?→?LUMO, but in the most stable dichlorvos-MAA it becomes the ππ* excitation of HOMO?→?LUMO?+?1; 3) Mulliken charges reveal that dichlorvos almost dissociates to Cl- and a cation in its S1 excitation state; 4) the phosphorescence spectra of dichlorvos-MAA are relatively weak.
Graphical Abstract The absorption and emission spectra of dichlorvos and the dichlorvos-MAA complex in the molecularly imprinted recognition of dichlorvos were investigated systematically in methanol, water, and chloroform as solvents.
The diffusion coefficients of 14 n-alkanes (ranging from methane to n-tetradecane) in liquid and supercritical methanol at infinite dilution (at a pressure of 10.5 MPa and at temperatures of 299 K and 515 K) were deduced via molecular dynamics simulations. Values for the radial distribution function, coordination number, and number of hydrogen bonds were then calculated to explore the local structure of each fluid. The flexibility of the n-alkane (as characterized by the computed dihedral distribution, end-to-end distance, and radius of gyration) was found to be a major influence and hydrogen bonding to be a minor influence on the local structure. Hydrogen bonding reduces the flexibility of the n-alkane, whereas increasing the temperature enhances its flexibility, with temperature having a greater effect than hydrogen bonding on flexibility.
Graphical abstract The flexibility of the alkane is a major influence and the hydrogen bonding is a minor influence on the first solvation shell; the coordination numbers of long-chain n-alkanes in the first solvation shell are rather low
In this article, we explore the capacity of formed Schiff base complexes to trap metal atoms or ions, using their aromatic ends. The intrinsic geometry of each complex defines the process of substitution. Two cases were studied; one involving a trans Schiff base complex and the other considering how a salen ligand, with nickel systems traps chromium. We also assessed the nature of the new bonds and the frontier molecular orbitals.
Spin–spin coupling constants in water monomer and dimer have been calculated using several wave function and density functional-based methods. CCSD, MCSCF, and SOPPA wave functions methods yield similar results, specially when an additive approach is used with the MCSCF. Several functionals have been used to analyze their performance with the Jacob’s ladder and a set of functionals with different HF exchange were tested. Functionals with large HF exchange appropriately predict 1JOH, 2JHH and 2hJOO couplings, while 1hJOH is better calculated with functionals that include a reduced fraction of HF exchange. Accurate functionals for 1JOH and 2JHH have been tested in a tetramer water model. The hydrogen bond effects on these intramolecular couplings are additive when they are calculated by SOPPA(CCSD) wave function and DFT methods.
The catalytic pyrolysis pathways of carbonyl compounds in coal were systematically studied using density functional theory (DFT), with benzaldehyde (C6H5CHO) employed as a coal-based model compound and ZnO, γ-Al2O3, and CaO as catalysts. The results show that the products of both pyrolysis and catalytic pyrolysis are C6H6 and CO. However, the presence of any of the catalysts changes the reaction pathway and reduces the energy barrier, indicating that these catalysts promote C6H5CHO decomposition.
Graphical abstract The presence of catalysts changes the reaction pathway and the energy barrier decreases in the order Ea (no catalyst)> Ea (CaO)> Ea (γ-Al2O3)> Ea (ZnO), indicating that these catalysts promote C6H5CHO decomposition.
In this article, we explore, both theoretically and experimentally, the general reactivity of alkyl hydrogeno-phenylphosphinates with alcohols. We show that alcohol molecules act exclusively as nucleophilic species, and add to alkyl hydrogeno-phenylphosphinates, leading to pentacoordinated intermediates. These intermediates are shown to subsequently competitively undergo alcohol eliminations and/or Berry pseudorotations. This offers several possible routes for racemizations and/or alcohol exchange reactions. Transition standard Gibbs free energies predicted from DFT calculations for the overall alcohol exchange mechanism are shown to be compatible with those experimentally measured in case ethanol reacts with ethyl hydrogeno-phenylphosphinate (134.5～136.0 kJ mol?1 at 78 °C).
Based on dissipative particle dynamics (DPD) methods and experimental data, we used an empirical relationship between the DPD temperature and the real temperature to build a model that describes the viscosity of molten TNT fluids. The errors in the predicted viscosity based on this model were no more than 2.3 %. We also studied the steady-state shear rheological behavior of molten TNT fluids containing nanoparticles (“nanofluids”). The dependence of the nanofluid viscosity on the temperature was found to satisfy an Arrhenius-type equation, η?=?AeB/T, where B, the flow activation energy, depends on particle content, size, and shape. We modified the Einstein-type viscosity model to account for the effects of nanoparticle solvation in TNT nanofluids. The resulting model was able to correctly predict the viscosities of suspensions containing nano- to microsized particles, and did not require any changes to the physical background of Einstein’s viscosity theory.
