Lauricella hypergeometric series $$F_A^{(n)}$$ F A ( n ) over finite fields

The Ramanujan Journal - In this paper, we develop a finite field analogue for one of the Lauricella series, $$F^{(n)}_A$$ . Extending results of Greene, a finite field analogue for the multinomial...     

Control over Kinetic and Thermodynamically Driven Pathways of Crystallization to Yield Cofacial and Slipped-Stack Dimers in Single Crystals

Control over the molecular packing in the solid state is of utmost importance in regulating the bulk optical properties of organic semiconductors. The electronic coupling between the molecules makes it possible to improve the properties of the bulk materials. This work reports an example of control over the selective formation of polymorphic single crystals of donor–acceptor-type small-molecule compound 25TR by 1) kinetic or 2) thermodynamic course of crystallisation to yield slipped stack (S) and cofacial (C) dimers in the single crystals. The distinct optical characteristics of the C-dimer and S-dimer are summarised. Both forms show significant excitonic interactions in the solid state, and the S-dimeric form has strong yellowish orange fluorescence, whereas the C-dimeric form is non-fluorescent in the crystalline state. DFT calculations and differential scanning calorimetric experiments revealed that the C-dimer polymorph is the thermodynamically stable form with a free energy offset of 0.43 eV in comparison with the S-dimer. Interestingly, the thermodynamically driven non-fluorescent single crystal was found to be convertible to its fluorescent form irreversibly by thermal trigger. The charge-carrier-transport characteristics of these two polymorphs were computed by using the Marcus–Hush formalism. The computations of the charge-carrier-transport behaviour revealed that the S-dimer ( 25TR_(R) ) is ambipolar, whereas the C-dimer ( 25TR_(Y) ) is predominantly n-type.     

A theoretical investigation of Zn?Zn and Be?Be one electron bond

Attachment of one electron to 1,2-diBeX-benzene and 1,2-diZnX-benzene derivatives leads to the formation of stronger Be Be and Zn Zn interaction compared to the neutral one. This is reflected in the dramatic shortening of the Be Be and Zn Zn distance. The formation of these 2-center-1-electron bonds have also been confirmed by topological survey of electron density using quantum theory of atoms in molecules and electron localization function. The formation of these bonds is expected to render stability to these radical anions. These radical anions are stable toward electron detachment and computed bond dissociation energy values are also significant.     

Perturbing π-clouds with Substituents to Study the Effects on Reaction Dynamics of gauche-1,3-Butadiene to Bicyclobutane Electrocyclization

The conical intersection (CI) governs the ultra-fast relaxation of excited states in a radiationless manner and are observed mainly in photochemical processes. In the current work, we investigated the effects of substituents on the reaction dynamics for the conversion of gauche-1,3-butadiene to bicyclobutane via photochemical electrocyclization. We incorporated both electron withdrawing (−F) and donating (−CH₃) groups in the conjugated system. In our study, we optimized the minimum energy conical intersection (MECI) geometries using the multi-configurational state-averaged CASSCF approach, whereas, to study the ground state reaction pathways for the substituted derivatives, dispersion corrected, B3LYP-D3 functional was used. The non-adiabatic surface hopping molecular dynamics simulations were performed to observe the behaviour of electronic states involved throughout the photoconversion process. The results obtained from the multi-reference second-order perturbation correction of energy at the XMS-CASPT2 level of theory, topography analysis, and non-adiabatic dynamics suggest that the −CH₃ substituted derivatives can undergo faster thermal conversion to the product in the ground state with a smaller activation energy barrier compared to −F substituted derivative. Our study also reveals that the GBUT to BIBUT conversion follows both conrotatory and disrotatory pathways, whereas, on substitution with −F or −CH₃, the conversion proceeds via the conrotatory pathway.     

Hetero-Polar Sextuple Bond: A Relativistic Quantum Chemical Study**

Number of bonds formed by sharing an electron pair between two atoms is not restricted to one, it can go beyond four and six is the maximum. While homopolar sextuple bond in Mo₂ and W₂ has been reported, such a high bond order in heteropolar diatomics has remained elusive. In the pursuit of the sextuple bond in polar diatomics, the present study depicts the existence of such multiple bonds in Rhodium-Scandium hetero-diatom based on relativistic quantum chemical calculations. The bonding comprises of three normal electron sharing covalent bonds and three dative covalent bonds.     

DFT study of CO adsorption on neutral and charged Pd<Subscript>n</Subscript>(n = 1–7) clusters

Density functional calculations have been performed to investigate CO adsorption on neutral, cationic and anionic Pd_n (n=1–7) clusters. From the results, it is observed that the binding of CO molecule to neutral and cationic palladium clusters takes place via 1-, 2- and 3-fold coordination. On the other hand, only terminal adsorption of CO molecule is possible in anionic clusters barring bridging adsorption in Pd₇ ^- cluster.     

Ion Interactions with a New Ditopic Naphthalimide‐Based Receptor: A Photophysical,NMR and Theoretical (DFT) Study

A new multi‐component chemosensor system comprising a naphthalimide moiety as fluorophore is designed and developed to investigate receptor–analyte binding interactions in the presence of metal and non‐metal ions. A dimethylamino moiety is utilized as receptor for metal ions and a thiourea receptor, having acidic protons, for binding anions. The system is characterized by conventional analytical methods. The absorption and fluorescence spectra of the system consist of a broad band typical for an intramolecular charge transfer (ICT). The effects of various metal‐ion additives on the spectral behavior of the present sensor system are examined in acetonitrile. It is found that among the metal ions studied, alkali/alkaline earth‐metal ions and transition‐metal ions modulate the absorption and fluorescence spectra of the system. As an additional feature, the anion signaling behavior of the system in acetonitrile is studied. A decrease in fluorescence efficiency of the system is observed upon addition of fluoride and acetate anions. Fluorescence quenching is most effective in the case of fluoride ions. This is attributed to the enhancement of the photoinduced electron transfer from the anion receptor to the fluorophore moiety. Hydrogen‐bond interactions between the acidic NH protons of the thiourea moiety and the F^? anions are primarily attributed to the fluoride‐selective signaling behavior. Interestingly, a negative cooperativity for the binding event is observed when the interactions of the system are studied in the presence of both Zn²⁺ and F^? ions. NMR spectroscopy and theoretical calculations are also carried out to better understand the receptor–analyte binding.     

Nitric oxide reactivity of copper(II) complexes of bidentate amine ligands: effect of chelate ring size on the stability of a [Cu(II)-NO] intermediate

Three copper(II) complexes, 1, 2, and 3 with L(1), L(2) and L(3) [L(1) = 2-(2-aminoethyl)-pyridine; L(2) = 2-(N-ethyl-2-aminoethyl)-pyridine; L(3) = 3,3'-iminobis(N,N-dimethylpropylamine)], respectively, were synthesized and characterized. Addition of nitric oxide gas to the degassed acetonitrile solution of the complexes were found to result in the reduction of the copper(II) center to copper(I). In cases of complexes 1 and 2, the formation of the [Cu(II)-NO] intermediate prior to the reduction of Cu(II) was evidenced by UV-visible, solution FT-IR and X-band EPR spectroscopic studies. However, for complex 3, the formation of [Cu(II)-NO] has not been observed. DFT calculations on the [Cu(II)-NO] intermediate generated from complex 1 suggest a distorted square pyramidal geometry with the NO ligand coordinated to the Cu(II) center at an equatorial site in a bent geometry. In the case of complex 1, the reduction of the copper(II) center by nitric oxide afforded ligand transformation through diazotization at the primary amine site in acetonitrile solution; whereas, in an acetonitrile-water mixture, it resulted in 2-(pyridine-2-yl)ethanol. On the other hand, in cases of complexes 2 and 3, it was found to yield N-nitrosation at the secondary amine site in the ligand frameworks. The final organic products, in each case, were isolated and characterized by various spectroscopic studies.     

Copper(ii) complexes as turn on fluorescent sensors for nitric oxide

Two copper(ii) complexes, 1 and 2, of two tridentate N-donor ligands, L(1) and L(2) [L(1) = dansyl derivative of bis-[3-(dimethylamino)-propyl]amine; L(2) = dansyl derivative of dipropylenetriamine] were synthesized and characterized. The quenched fluorescence intensity of complexes 1 and 2, in degassed methanol or aqueous (buffered at pH 7.2) solution, was found to reappear on exposure to nitric oxide. This is attributed to the reduction of paramagnetic Cu(ii) center by nitric oxide to diamagnetic Cu(i).