DFT and CIS(D) theoretical study on the ground and excited states of pentanitrogen cation

Different isomers of N₅⁺ were modeled at DFT(PBE0)/aug-cc-pV(Q + d)Z, and their ground(transition) state characteristics were assessed through frequency calculations. Single-point energies were accomplished at PBE0/aug-cc-pV(5 + d)Z. Nonlinear optical susceptibilities (NLO) of isomers were accomplished using Firefly, while the linear optical invariant was examined using the finite-field method, Firefly, and modified dipole field tensor in the presence of two different screening factors. The excited states, singlets and triplets, of were modeled at the CIS and CIS(D) and then their optical parameters were estimated at TDFT(PBE0)/aug-cc-pV(Q + d)Z using Firefly. The singlet is found the most stable isomer, with the inversional rate constant larger than that of the Cs isomer and high energy barrier with the triplet counterpart. Isomers 2 , 3 , and 4 are found local minima, while 5 and 6 are saddle points: transition states between equivalent invertomers. Energy calculations of the singlet and triplet isomers were in excellent agreement with the literature. An excellent correlation is found between the average polarizability and the impulse factor. Substantial variations were found between the singlet and triplet excited states in terms of energy, geometry, and optical properties from one side and with from the other side. Reactivity indices showed that N1 and N5 are the optimum nucleophilic and electrophilic reactivity sites.     

Dynamical Jahn-Teller effect in the first excited

Jahn-Teller effect of C₆₀ monoanion in the first electronically excited states was theoretically investigated. The orbital vibronic coupling parameters for t_1g next lowest unoccupied molecular orbitals were derived from the Kohn-Sham orbital levels calculated using a frozen phonon approach with both hybrid B3LYP and CAM-B3LYP functionals, which take long-range interaction correction into consideration. With these coupling parameters, the vibronic states of first excited were derived by exactly diagonalizing dynamical Jahn-Teller Hamiltonian. The results showed that dynamical Jahn-Teller effects are more significant in the first excited than those in the ground electronic states. This work also clarified that CAM-B3LYP gives results closer to experimental data than B3LYP.     

Unexpected properties of non‐autoionizing doubly excited states of the H2 molecule

We present accurate calculations of the non‐autoionizing and doubly excited states of the H₂ molecule using full configuration interaction with Hartree–Fock molecular orbitals and Heitler–London atomic orbitals. We consider the united atom configurations from He(2p2p) up to He(2p8g) and dissociation products from H₂(2p + 2p) up to H₂(2p + 6?). Born–Oppenheimer calculations are carried out with extended and optimized Slater‐type orbitals for a total of 40 states, 10 for each symmetry, covering the internuclear distances from the united atom to dissociation, which, for some states, is reached beyond 100 a₀. Occurrences of repulsive states cleanly interlaced between bound states with many vibrational levels are reported. Some of the potential minima are deep enough to accommodate many vibrational levels (up to 50). Noteworthy large equilibrium minima, like R_eq = 46.0 a₀ in the state dissociating as (2p + 6h) and with 18 vibrational levels. The occurrence of vertical excitations from the singly excited manifolds is analyzed. Several states present double minima generated by avoided crossings, some with a strong ionic character. © 2016 Wiley Periodicals, Inc.     

Extremal Wiener and Kirchhoff indices of globular caterpillars

The Wiener and Kirchhoff indices of a graph G are two of the most important topological indices in mathematical chemistry. A graph G is called to be a globular caterpillar if G is obtained from a complete graph K _s with vertex set {v₁,v₂,…, v _s} by attaching n _i pendent edges to each vertex v _i of K _s for some positive integers s and n₁,n₂,…,n _s, denoted by . Let be the set of globular caterpillars with n vertices (). In this article, we characterize the globular caterpillars with the minimal and maximal Wiener and Kirchhoff indices among , respectively.     

How does the pH influences the Ru-NO coordination compounds?

The pH influence has important role in the bioavailability of coordination compounds. fac-[Ru(NO)Cl₂(κ³N⁴,N⁸,N¹¹[1-carboxypropyl]cyclam)]⁺, 1 , and the species found at different pHs, 2 - 4 , were investigated. One series of computational methodologies has been used to investigate these compounds. One special highlight is to interacting quantum atoms method, where the total interaction energy, , between two atoms has been used as base to estimate the chemical bonds strength. The deprotonation of -CO₂H, 1 ➔ 2 (pK_a = 3.3), creates a hydrogen bond in the complex 2 , N( 3 )-H⋯ ·OCO⁻, with a more favorable than the presents in 1 , N( 3 )-H⋯ ·OCOH. There are no changes in in Ru-NO bond. The second deprotonation occurs in the N(2) atom of the cyclam group, 2 ➔ 3 (pK_a = 8.0). It promotes an increase in the covalent character of Ru-N( 2 ). In contrast, there is no changes in Ru-N( 5 )O bond. For higher pHs, there is a 3 ➔ 4 equilibrium (pK_a = 11.5) and the conversion of Ru-N( 5 )O for Ru-N( 5 )O₂. The Ru-N( 5 ) of 4 shows a larger ionic character than 3 . Thus, Ru-NO in 1 - 4 has worthy stability about a large pH range, showing potential application as NO scavengers.     

He2@C60: Thoughts of the concept of a molecule and of the concept of a bond in quantum chemistry

We present a broad palette of discussions of the concepts of a molecule and a chemical bond that always lay down behind all computational modeling in quantum chemistry and of the endohedral fullerene He₂@C₆₀ in particular. For this purpose, we offer the definition of quantum chemistry as composed of three ingredients. Each of them is illustrated by its particular concept, either that of a molecule or a bond. The third, computational ingredient is tackled to resolve the bonding manifold of He₂@C₆₀ and to demonstrate that van‐der‐Waals binding of He? He is converted within He₂@C₆₀ into a stronger bond due to that C₆₀ acts as an electronic buffer and [He₂] moiety mimics a fractionally charged . Experimental fingerprints of He₂@C₆₀ are computed. © 2015 Wiley Periodicals, Inc.     

Ionized water clusters,n = 2 to 6: A high-accuracy study of structures and energetics

Ionized water clusters, , have been of remarkable interest owing to their crucial roles in many chemical and biological processes. Small cationic water clusters , n = 2 to 6 serve as reasonable models for understanding the nature of the ionized water. In this study, employing high-level ab initio quantum chemical methods, such as the density-fitted orbital-optimized linearized coupled-cluster doubles (DF-OLCCD), coupled-cluster singles and doubles (CCSD), and coupled-cluster singles and doubles with perturbative triples [CCSD(T)], a high-accuracy study of structures and energetics for cationic water clusters [, n = 2-6] is presented. In this study, 2 dimer, 8 trimer, 18 tetramer, 23 pentamer, and 25 hexamer clusters are reported. Most of the structures considered are reported for the first time. Relative, binding, and vertical attachment energies (VAEs), for the first time, are presented at the complete basis set (CBS) limit, extrapolating energies of the aug-cc-pVTZ and aug-cc-pVQZ basis sets, to provide the most accurate energetics to date. Our results demonstrate that as cluster size increases, the VAE value decreases, which indicates that large-size clusters better compensate for the electron deficiency compared with small-size clusters. The VAE values for pentamer and hexamer clusters are 118.5 to 165.5 and 121.9 to 153.7 kcal mol⁻¹, respectively. Further, our binding energy results, at the CCSD(T)/CBS level, indicate strong bindings in cationic clusters due to hydrogen bond interactions. The average binding energy per water molecule varies from −16.6 to −21.8 kcal mol⁻¹ for the clusters considered. Hence, we present the most extensive and accurate study on ionized water clusters to date. Further, our results indicate that the DF-OLCCD method is very promising for ionic molecular clusters, and its accuracy approaches the CCSD(T) quality. The inexpensive analytic gradients of DF-OLCCD, compared with CCSD(T), make it very helpful for high-accuracy studies of molecular geometries.     

Subspace effective potential theory for configuration interaction

In this article we present an approach which combines the configuration interaction methodology and orbitals derived via single particle equations with a local potential V_eff, the variational parameters of which are determined by minimizing the so‐called subspace functional instead of the traditional single energy functional . In this way ground and excited states orbitals are put on equal footing. The V_eff is restricted to have the form of a model potential expressed in terms of the external potential. One of the advantages of the present direct mapping formulation, is that the effective potential, V_eff, has the symmetry of the external potential. Applications are focused mainly on excited states of the HeH and BeH molecules having spatial and spin symmetries as those of the ground one. © 2016 Wiley Periodicals, Inc.     

On the normalized Laplacian of Möbius phenylene chain and its applications

Let denote a molecular graph of linear [n] phenylene with n hexagons and n squares, and let the Möbius phenylene chain be the graph obtained from the by identifying the opposite lateral edges in reversed way. Utilizing the decomposition theorem of the normalized Laplacian characteristic polynomial, we study the normalized Laplacian spectrum of , which consists of the eigenvalues of two symmetric matrices ℒ _R and ℒ _Q of order 3n. By investigating the relationship between the roots and coefficients of the characteristic polynomials of the two matrices above, we obtain an explicit closed-form formula of the multiplicative degree-Kirchhoff index as well as the number of spanning trees of . Furthermore, we determine the limited value for the quotient of the multiplicative degree-Kirchhoff index and the Gutman index of .     

Electronic Structure of the Low-Lying States of the Triatomic MoS2 Molecule: The Building Block of 2D MoS2

Molybdenum disulfide (MoS₂) is the building component of 1D-monolayer, 2D-layered nanosheets and nanotubes having many applications in industry, and it is detected in various molecular systems observed in nature. Here, the electronic structure and the chemical bonding of sixteen low-lying states of the triatomic MoS₂ molecule are investigated, while the connection of the chemical bonding of the isolated MoS₂ molecule to the relevant 2D-MoS₂, is emphasized. The MoS₂ molecule is studied via DFT and multireference methodologies, i. e., MRCISD(+Q)/aug-cc-pVQZ(−PP)_Mo. The ground state, ³B₁, is bent (Mo−S=2.133 Å and ϕ(SMoS)=115.9°) with a dissociation energy to atomic products of 194.7 kcal/mol at MRCISD+Q. In the ground and in the first excited state a double bond is formed between Mo and each S atom, i. e., . These two states differ in which d electrons of Mo are unpaired. The Mo−S bond distances of the calculated states range from 2.108 to 2.505 Å, the SMoS angles range from 104.1 to 180.0°, and the Mo−S bonds are single or double. Potential energy curves and surfaces have been plotted for the ³B₁, ⁵A₁ and ⁵B₁ states. Finally, the low-lying septet states of the triatomic molecule are involved in the material as a building block, explaining the variety of its morphologies.     

Theoretical study on the electronic structures and optical properties of blue‐green and blue phosphorescent iridium(III) complexes with tetraphenylimidodiphosphinate ligand

The electronic structures and photophysical properties of five iridium(III) complexes Ir(tfmppy)₂(tpip) (1), Ir(dfppy)₂(tpip) (2), Ir(afCNppy)₂(tpip) (3), Ir(CNpyN₃)₂(tpip) (4), and Ir(2fphpta)₂(tpip) (5) [where tfmppy = 4‐trifluoromethylphenylpyridine; dfppy =4,6‐difluorophenylpyridine; afCNppy = 6‐fluoro‐4‐octyloxy‐5‐cyano‐phenylpyridine; CNpyN₃ = 2‐(4‐cyano‐phenyl)‐[1,2,3]‐triazole; 2fphpta=2‐(2,6‐difluoro‐phenyl‐[1,2,4]‐triazol‐3‐yl)‐pyridine; tpip=tetraphenylimido‐diphosphinate] have been investigated by using density functional theory (DFT) methods and time‐dependent DFT ones, aiming at elucidating the influences of different substituents and cyclometalated ligands on the emission properties and quantum yield. The calculated results revealed that the different substituents in 1 ‐ 3 have a great influence on the energy levels, in particular highest occupied molecular orbital. Meanwhile, we have also get a further insight into the reason for different phosphorescence quantum yields of the studied complexes. The higher quantum yield (Φ) reported for 1 was found to be closely related to both its smaller S₁–T₁ splitting energy ( ) and larger transition electric dipole moment ( ) upon the S₀ → S₁ transition. Complex 5 is expected to be a potential candidate for blue‐emitting material with good organic light‐emitting diodes performances. We propose that the optical properties of this class of materials can be tuned by the modifications of the cyclometalated ligands. © 2013 Wiley Periodicals, Inc.     

Geometric and electronic structures of silicon fluorides (N = 4 – 6) and potential energy surfaces for dissociation reactions → SiF4 + F– and → + F–

The geometric and electronic structures of a series of silicon fluorides (n = 4 ? 6) were computationally studied with the aid of density functional theory (DFT) method with B3LYP and M06‐2X functionals and coupled cluster (CCSD and CCSD(T)) methods with 6‐311++G(d,p) basis set. The nature of the Si‐F bonds in these compounds was analyzed in the framework of the natural bond orbital theory and natural resonance theory. Energy characteristics (heats of reactions and energy barriers) of the dissociation reactions → SiF₄ + F^– and → + F^– were calculated using the DFT and CCSD methods. The potential energy surface of elimination of a fluoride anion from has a specific topology with valley‐ridge inflection points corresponding to bifurcations of the minimal energy reaction path. © 2016 Wiley Periodicals, Inc.     

Comparison of triel bonds with different chalcogen electron donors: Its dependence on triel donor and methyl substitution

The complexes between R₃Tr (Tr = B, Al, and Ga; R = H, F, Cl, and Br) and H₂X (X = O, S, and Se) were theoretically studied. The interaction energies of R₃Al⋯H₂X and R₃Ga⋯H₂X are consistent with the electronegativity of the halogen atom R (R ≠ H), but an opposite dependence is found for R₃B⋯H₂X. The triel bond of R₃Tr⋯H₂X is weaker for the heavier chalcogen donor. The dependence of triel bonding strength on the triel atom is complicated, depending on the nature of R and X. The methyl substitution of H₂X causes a substantial increase in the interaction energy from −5.74 kcal/mol to −22.88 kcal/mol, and its effect is relevant to the nature of Tr, X, and R groups. For the S and Se donors, the increased percentage of interaction energy is almost the same due to the methyl substitution, which is larger than that of the O analogue. In most triel-bonded complexes, electrostatic dominates and polarization has comparable contribution. However, polarization plays a dominant role in R₃B⋯ and R₃B⋯ (R = Cl and Br; R′ = H and Me).     

Concerted stereodynamics of chemical changes: The branching selectivity in the photodissociation of asymmetric-top molecules,formic acid,and the cold reactivity of the H + H2 exchange reaction

This review article presents our recent examples of the branching selectivity in the photodissociation of asymmetric-top molecules, halothane CF₃CHBrCl and isohaloethane CF₂BrCHFCl. The former gave the unexpected branching ratio of ([Cl] + [Cl*])/([Br] + [Br*])$\approx$2 for the Br, Br* and Cl, Cl* atom fragmentations, meaning that the strongly bounded Cl-C bond gave twice favorable fragmentation, while the later isohaloethane gave almost the same value for all-atom fragmentations. We interpret this result due to the curve crossing of electronically excited states and the non-adiabatic interaction on the excited states. The bimodal vibrational distribution of the product CO fragment in the formic acid photodissociation at 193 nm evidenced a roaming signature by using the μs time-resolved Fourier-transform infrared emission spectra for the first time. We find the characteristic propensity rule in the time-dependent interaction potential to judge reactivity in the H + H₂ exchange reaction and the roaming-type of trajectory at temperature 3 K, by use of the impact-parameter dependent quasi-classical trajectory simulation, based on the present results, we conclude that reaction dynamics proceeds not only by the prerequisite of energy conservation but also by the timing of the time-dependent interaction potential which is very sensitive to the steric configuration of reaction intermediate, thus it may be called as the concerted stereodynamics.     

Virial relations in density embedding

The accuracy of charge-transfer excitation energies, solvatochromic shifts, and other environmental effects calculated via various density-embedding techniques depend critically on the approximations employed for the nonadditive noninteracting kinetic energy functional, . Approximating this functional remains an important challenge in electronic-structure theory. To assist in the development and testing of approximations for , we derive two virial relations for fragments in molecules. These establish separate connections between the nonadditive kinetic energies of the noninteracting and interacting systems of electrons, and quantities such as the electron-nuclear attraction forces, the partition (or embedding) energy and potential, and the Kohn-Sham potentials of the system and its parts. We numerically verify both relations on diatomic molecules.     

Improved description of the orbital relaxation effect by practical use of the self‐energy

The self‐energy shift in the orbital relaxation (OR) term of the polarization propagator complete through the second‐order is presented. In combination with the optimal damping parameter in the OR term, the modified propagator produces the excitation energy of the coupled‐cluster with singles and doubles (CCSD) accuracy. The self‐energy shift requires the floating‐point operation of , where N refers to the magnitude of the molecular size. Because the second‐order polarization propagator requires the floating‐point operation of , the additional computational effort to construct the self‐energy is negligibly small. Numerical results are shown for several molecules including glycine, 2,3,5,6‐tetrafluorobenzene, and naphthalene, and promising agreements with those of CCSD are confirmed within less than 0.2 eV. The basis set dependence is also tested for the water molecule using aug‐cc‐pV NZ (N = D–7), where this newly developed approach mimics the behavior of the CCSD values. The self‐energy shifting for the second‐order response matrix in combination with the use of a dumping parameter is efficiently implemented for calculations of medium‐sized molecular systems, including glycine and naphthalene. The developed approach provides CCSD‐like accuracy at a more affordable computational expense. © 2014 Wiley Periodicals, Inc.     

Explicitly correlated variational estimates of the energy levels of negative hydrogen ion under spatial confinement

Comprehensive investigations on the structural modifications of negative hydrogen ion within an impenetrable spherical domain has been performed in the framework of Ritz variational method. Electron correlation plays a major role in the formation of H^– ion. The Hylleraas‐type basis set expansion of wave function considered here incorporates the effect of electron correlation in an explicit manner. Energy values of and 1sn states of H^– ion within confined domain have been calculated. Although the singly excited states do not exist for a “free” H^– ion, well converged energy values of such states have been found within a wide range of confinement radius. The thermodynamic pressure felt by the ion inside the sphere is also estimated. The general trend shows successive destabilization of the excited energy levels with increase of pressure. The contribution of angular correlation in the energy values have been estimated. Evolution of and energy levels of H^– ion as quasi‐bound states are being reported.     

Triplet Generation Through Singlet Fission in Metal-Organic Framework: An Alternative Route to Inefficient Singlet-Triplet Intersystem Crossing

High quantum yield triplets, populated by initially prepared excited singlets, are desired for various energy conversion schemes in solid working compositions like porous MOFs. However, a large disparity in the distribution of the excitonic center of mass, singlet-triplet intersystem crossing (ISC) in such assemblies is inhibited, so much so that a carboxy-coordinated zirconium heavy metal ion cannot effectively facilitate the ISC through spin-orbit coupling. Circumventing this sluggish ISC, singlet fission (SF) is explored as a viable route to generating triplets in solution-stable MOFs. Efficient SF is achieved through a high degree of interchromophoric coupling that facilitates electron super-exchange to generate triplet pairs. Here we show that a predesigned chromophoric linker with extremely poor ISC efficiency (k_ISC) but form triplets in MOF in contrast to the frameworks that are built from linkers with sizable k_ISC but . This work opens a new photophysical and photochemical avenue in MOF chemistry and utility in energy conversion schemes.     

Theoretical study of the microhydration of 1-chloro and 2-chloro ethanol as a clue for their relative propensity toward dehalogenation

This work reports a computational analysis of hydrogen-bonded clusters of mono-, di-, tri-, and tetrahydrates of the chlorohydrins CH₃CHClOH (1ClEtOH) and CH₂ClCH₂OH (2ClEtOH). The goal of the study is to assess the role of the water solvent into the facilitation of the initial step for dehalogenation of these compounds, a process of interest in several contexts. Molecular orbital methods (MP2), density functional methods (B3LYP, M06, and ωB97X-D), and composite model chemistries (CBS-QB3, G4) were employed to investigate the structure, electronic distribution, and hydrogen-bonded structure of seven monohydrates, six dihydrates, five trihydrates, and five tetrahydrates of both species. Standard reaction enthalpy and standard Gibbs free reaction energy () were computed for all aggregates with respect to n independent water molecules and with respect to the dimer, trimer, and tetramer of water, respectively, in order to evaluate stability and hydrogen bonding network. The influence of the water chains on the length and vibrational frequencies, especially of the C Cl and O H bonds, was evaluated. Hydrogen bonding in the complexes is discussed at length.