GTI-space: the space of generalized topological indices

A new extension of the generalized topological indices (GTI) approach is carried out to represent “simple” and “composite” topological indices (TIs) in an unified way. This approach defines a GTI-space from which both simple and composite TIs represent particular subspaces. Accordingly, simple TIs such as Wiener, Balaban, Zagreb, Harary and Randić connectivity indices are expressed by means of the same GTI representation introduced for composite TIs such as hyper-Wiener, molecular topological index (MTI), Gutman index and reverse MTI. Using GTI-space approach we easily identify mathematical relations between some composite and simple indices, such as the relationship between hyper-Wiener and Wiener index and the relation between MTI and first Zagreb index. The relation of the GTI-space with the sub-structural cluster expansion of property/activity is also analysed and some routes for the applications of this approach to QSPR/QSAR are also given.     

Topological indices for molecular fragments and new graph invariants

Whereas the internal fragment topological index (IFTI) is calculated in the normal manner as for any molecule, the external fragment topological index (EFTI) is calculated so as to reflect the interaction between the excised fragment F and the remainder of the molecule (G-F). For selected topological indices (TIs), a survey of EFTI values, formulas and examples is presented. Some requirements as to the fragment indices are formulated and examined. In the discussion of the results, it is shown that for some TIs regularities exist in the dependence of EFTI values upon the branching of fragment F, or upon the marginal versus central position of the fragment F in the graph G. New vortex invariants can be computed as EFTI values for one-atom fragments over all graph vertices; by iteration, it is in principle possible to devise an infinite number of now vertex invariants.     

Benchmarking computational chemistry approaches on iminodiacetic acid

In the present study, theoretical harmonic vibrational frequencies (IR and Raman), carbon and proton NMR chemical shifts, geometric parameters, atomic charges (only for heteroatoms), reactivity indices (eLUMO, eHOMO, electronegativity, and hardness), and thermodynamical data (inner energy, enthalpy, Gibbs free energy, and entropy) of iminodiacetic acid (IDA) molecule have been investigated. We utilized ORCA software for B3LYP and HF (combined with Pople and Karlsruhe basis sets) calculations and MOPAC2016 software for semi-empirical calculations (AM1, PM3, and PM6). Theoretical vibrational frequencies and carbon and proton NMR chemical shifts have been compared with the corresponding experimental data. Although there was a strong correlation between the experimental and computational vibrational frequencies at low frequencies (<2200 cm^?1), the computational predictions of vibrational frequencies were unsuccessful at high frequencies (>2200 cm^?1). Distinctly, the studied computational approaches appeared to perform better in the prediction of carbon and proton NMR chemical shifts. Theoretical vibrational frequencies were also compared to each other to understand the impact of method choice (HF vs B3LYP D3 vs semi-empirical methods), dispersion correction (B3LYP D3 vs B3LYP), water solvation (SMD supplemented vs non-supplemented calculations), the family of basis set (Pople vs Karlsruhe basis sets), numbers of zeta (double vs triple zeta), polarization function (polarized vs nonpolarized basis sets), and diffusion function (diffusion supplemented vs non-supplemented basis sets). Moreover, geometric parameters, heteroatom charges, reactivity indices, and thermodynamical data produced by distinct computational approaches, as well, were compared to each other. Based on these comparisons, we detected critical factors (such as water solvation) acting on the computation of geometries, energies, and charges.     

Optimal characterization of structure for prediction of properties

Different topological and physicochemical parameters have been used to predict hydrophobicity (logP, octanol-water) of chemicals. We calculated a hydrogen bonding parameter (HB₁) and a large number of molecular connectivity and complexity indices for a diverse set of 382 molecules. It is known from earlier studies that topological indices (TIs) predict properties of congeneric sets reasonably well. Since HB₁ is an approximate quantifier of hydrogen bonding and has integral values, we used HB₁ to classify the diverse set into strongly and weakly hydrogen bonding subsets. In an attempt to examine the utility of Us in predicting properties of relatively similar groups of molecules, we carried out a correlation of logP with TIs for a subset (n = 139) of the original diverse set (n = 382) with a weak hydrogen bonding ability (HB₁ = 0). Results show that TIs give a better predictive model for the more homogeneous subset as compared to the diverse set of molecules.     

Spectroscopic studies of OCS-doped 4He clusters with 9-72 helium atoms: observation of broad oscillations in the rotational moment of inertia

High-resolution spectra of HeN-OCS clusters with N up to 39 in the microwave region and up to 72 in the infrared region were observed with apparatus-limited line widths of about 15 kHz and 0.001 cm(-1), respectively. The cold (approximately 0.2 K) clusters were produced in pulsed supersonic jet expansions of very dilute OCS + He mixtures and probed using a microwave Fourier transform spectrometer or a tunable infrared diode laser spectrometer. Consistent analyses of the microwave and infrared data yield band origins for the carbonyl stretching vibration, together with rotational parameters for the ground and excited vibrational states. The rotational constant, B, passes through a minimum at N = 9 and then rises as the He atoms uncouple from the OCS rotational motion as a result of superfluid effects. There are broad unexpected oscillations in B, with maxima at N = 24 and 47 and minima at N = 36 and 62. The change in B upon vibrational excitation, which is negative for the OCS molecule, converges to positive values for N > 15. These results help to bridge the gap between individual molecules and bulk matter with atom-by-atom resolution over a significant range of cluster sizes.     

Optimal neighbor selection in molecular similarity: comparison of arbitrary versus tailored prediction spaces

Three classes of arbitrary quantitative molecular similarity analysis (QMSA) methods have been computed using atom pairs (APs), topological indices (TIs), and principal components (PCs) derived from topological indices. Tailored QMSA models have been developed from TIs selected through ridge regression. K-nearest neighbor (kNN) based estimation has been applied to all of the methods to estimate normal vapor pressure (p(vap)) and water solubility (sol) for a set of 194 chemicals. Results show that the tailored QMSA methods are superior to arbitrary similarity methods in estimating both of these properties for the given set of chemicals.     

Comparison of the Topological and Dynamic Characteristics of Molecules for Calculating Retention Indices of Organic Compounds

This paper reports on a comparative analysis of the linear correlation equations relating the gas-chromatographic retention indices (RI) of several groups of isomeric organic compounds to the topological (Wiener and Hosoya indices) and dynamic (intramolecular energies estimated by molecular dynamic methods and the vibrational components of this energy estimated with simple models) parameters of molecules. It is shown that the choice of one of these parameters does not ensure the best approximation to RI, since the results depend on the chemical nature of substances. Correlations between all of the above quantities have been established. The correlations serve as a basis for physicochemical interpretation of the topological parameters of molecules as quantities proportional to the intramolecular vibrational and rotation energies.     

Four new topological indices based on the molecular path code

The sequence of all paths pi of lengths i = 1 to the maximum possible length in a hydrogen-depleted molecular graph (which sequence is also called the molecular path code) contains significant information on the molecular topology, and as such it is a reasonable choice to be selected as the basis of topological indices (TIs). Four new (or five partly new) TIs with progressively improved performance (judged by correctly reflecting branching, centricity, and cyclicity of graphs, ordering of alkanes, and low degeneracy) have been explored. (i) By summing the squares of all numbers in the sequence one obtains Sigmaipi(2), and by dividing this sum by one plus the cyclomatic number, a Quadratic TI is obtained: Q = Sigmaipi(2)/(mu+1). (ii) On summing the Square roots of all numbers in the sequence one obtains Sigmaipi(1/2), and by dividing this sum by one plus the cyclomatic number, the TI denoted by S is obtained: S = Sigmaipi(1/2)/(mu+1). (iii) On dividing terms in this sum by the corresponding topological distances, one obtains the Distance-reduced index D = Sigmai{pi(1/2)/[i(mu+1)]}. Two similar formulas define the next two indices, the first one with no square roots: (iv) distance-Attenuated index: A = Sigmai{pi/[i(mu + 1)]}; and (v) the last TI with two square roots: Path-count index: P = Sigmai{pi(1/2)/[i(1/2)(mu + 1)]}. These five TIs are compared for their degeneracy, ordering of alkanes, and performance in QSPR (for all alkanes with 3-12 carbon atoms and for all possible chemical cyclic or acyclic graphs with 4-6 carbon atoms) in correlations with six physical properties and one chemical property.     

Structural,electronic properties and intramolecular hydrogen bonding of substituted 2-[(E)-imino methyl] benzenethiol in ground and first excited state by quantum chemical methods

Quantum chemical calculations of geometric structure, the intramolecular hydrogen bond, harmonic vibrational frequencies, NMR spin–spin coupling constants, and physical properties such as chemical potential and chemical hardness of the 2-(E)-imino methyl benzenethiol and its nineteen derivatives were carried out using density functional theory (DFT/B3LYP/6-311++G**) method in the gas phase and the water solution. Furthermore, the topological properties of the electron density distributions for S–H···N intramolecular hydrogen bond have been analyzed in terms of the Bader’s theory of atoms in molecules (AIM). Natural bond orbital (NBO) analysis also performed for better understanding the nature of intramolecular interactions, the results of analysis by quantum theory of AIM and NBO method fairly supported the DFT results. Besides, MEP was performed by the DFT method. On the other hand, the aromaticity of the formed ring has been measured using several well-established indices of aromaticity such as nucleus-independent chemical shift, harmonic oscillator models of the aromaticity, para-delocalization index, average two-center indices, and aromatic fluctuation index. Also, the excited-state properties of intramolecular hydrogen bonding in these systems have been investigated theoretically using the time-dependent DFT method.     

Electronic structures, intramolecular interactions, and aromaticity of substituted 1-(2-iminoethylidene) silan amine: a density functional study

The intramolecular hydrogen bond, molecular structure, π electrons delocalization, and vibrational frequencies in 1-(2-iminoethylidene) silan amine and its derivatives have been investigated by means of density functional method with 6-311++G** basis set, in gas phase, water, and carbon tetrachloride solutions. The obtained results showed that the hydrogen bond strength is mainly governed by resonance variations inside the chelate ring induced by the substituent groups. Furthermore, the topological properties of the electron density distributions for N–H···N intramolecular hydrogen bond were analyzed in terms of the Bader's theory of atoms in molecules. On the other hand, the aromaticity of the ring formed is measured using several well-established indices of aromaticity such as nucleus-independent chemical shift, harmonic oscillator models of the aromaticity, para-delocalization index, average two-center indices, aromatic fluctuation index, and π-fluctuation aromatic index. Natural population analysis data, the electron density and Laplacian properties, as well as γ(NH) and ν(NH) were further used for estimation of the hydrogen bonding interactions and the forces driving their formation.     

N6(2+) and N4(2+) dications and their n(12) and n(10) azido derivatives: DFT/GIAO-MP2 theoretical studies.

The structures and energies of N(6)(2+) and N(4)(2+) were calculated by using the density functional theory method at the B3LYP/cc-aug-pVTZ level. The C(2)(h)() symmetric form 1 and D(infinity)(h) form 5 were found to be the stable minima for N(6)(2+) and N(4)(2+), respectively. Dissociation of 1 into 5 and N(2) was computed to be endothermic by 25.1 kcal/mol. (15)N NMR chemical shifts and vibrational frequencies of 1 and 5 were also calculated. Interactions of 1 and 5 with azide ions were also probed representing N(12) and N(10).     

Structure and conformational properties of N-pentafluorosulfur(sulfuroxide difluoride imide) SF5N=S(O)F2: vibrational analysis, gas electron diffraction, and quantum chemical calculations

The molecular structure and conformational properties of N-pentafluorosulfur(sulfuroxide difluoride imide), SF5N=S(O)F2, have been studied by vibrational spectroscopy (IR (gas) and Raman (liquid)), by gas electron diffraction (GED), and by quantum chemical calculations (MP2 and B3LYP with (6-31G(d) and 6-311+G(2df) basis sets). According to GED, the prevailing conformer possesses a syn structure (N-SF5 bond synperiplanar with respect to the bisector of the SF2 group). Splitting of the symmetric N=S=O stretching vibration in gas and liquid spectra demonstrates the presence of a second conformer (11(5)%) with anticlinal orientation of the N-SF5 bond according to quantum chemical calculations. The geometric structure, conformational properties, and vibrational frequencies are well reproduced by quantum chemical calculations.     

Density functional study of indole–pyrrole heterodimer potential energy hypersurface

A density‐functional study of indole–pyrrole heterodimer potential energy hypersurface (PES) was performed. Eight stationary points were located on the B3LYP/6‐31++G(d,p) PES, three of which correspond to real minima, all of them being characterized with an N? H … π type hydrogen bonding. In two of these minima (the local ones), pyrrole subunit acts as a hydrogen bond proton donor, while the global minimum corresponds to indole–H … π(‐pyrrole) arrangement. Besides the interaction and dissociation energies corrected for BSSE and the monomer relaxation energies and the relevant structural parameters, anharmonic N? H and N? H … π vibrational frequencies were calculated for various N? H oscillators involved in this interaction from the 1‐D DFT vibrational potentials. On the basis of anharmonic vibrational frequency analysis, it was concluded that the two types of N? H … π hydrogen bonded dimers (indole vs. pyrrole being a proton donor) should be distinguishable with spectroscopic methods. Various contributions to the overall anharmonic frequency shifts upon hydrogen bonding were calculated and discussed as well. The charge field perturbation (CFP) technique was employed to study the electrostatic + polarization influence of the proton accepting unit on the N? H(… π) vibrational potential. The second‐order perturbation theory analysis (SOPT) of the Fock matrix (i.e., its Kohn–Sham analog) within the natural bond orbital (NBO) basis, as well as various NBO deletion analyses revealed an essentially one‐directional charge transfer (CT) of a π(C? C) → σ*(N? H) type in the case of all three minima. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003