Multiple zigzag chains Zm,n of length
and width
constitute an important class of regular graphene flakes of rectangular shape. The physical and chemical properties of these basic pericondensed ...benzenoids can be related to their various topological invariants, conveniently encoded as the coefficients of a combinatorial polynomial, usually referred to as the ZZ polynomial of multiple zigzag chains Zm,n. The current study reports a novel method for determination of these ZZ polynomials based on a hypothesized extension to John-Sachs theorem, used previously to enumerate Kekulé structures of various benzenoid hydrocarbons. We show that the ZZ polynomial of the Zm,n multiple zigzag chain can be conveniently expressed as a determinant of a Toeplitz (or almost Toeplitz) matrix of size m2×m2 consisting of simple hypergeometric polynomials. The presented analysis can be extended to generalized multiple zigzag chains Zkm,n, i.e., derivatives of Zm,n with a single attached polyacene chain of length
. All presented formulas are accompanied by formal proofs. The developed theoretical machinery is applied for predicting aromaticity distribution patterns in large and infinite multiple zigzag chains Zm,n and for computing the distribution of spin densities in biradical states of finite multiple zigzag chains Zm,n.
The Criegee intermediates are carbonyl oxides postulated to play key roles in the reactions of ozone with unsaturated hydrocarbons; these reactions constitute an important mechanism for the removal ...of unsaturated hydrocarbons and for the production of OH in the atmosphere. Here, we report the transient infrared (IR) absorption spectrum of the simplest Criegee intermediate CH₂OO, produced from CH₂I + O₂ in a flow reactor, using a step-scan Fourier-transform spectrometer. The five observed bands provide definitive identification of this intermediate. The observed vibrational frequencies are more consistent with a zwitterion rather than a diradical structure of CH₂OO. The direct IR detection of CH₂OO should prove useful for kinetic and mechanistic investigations of the Criegee mechanism.
We show-to our own surprise-that total electronic energies for a family of
×
rectangular graphene flakes can be very accurately represented by a simple function of the structural parameters
and
with ...errors not exceeding 1 kcal/mol. The energies of these flakes, usually referred to as multiple zigzag chains
(
,
), are computed for
,
< 21 at their optimized geometries using the DFTB3 methodology. We have discovered that the structural parameters
and
(and their simple algebraic functions) provide a much better basis for the energy decomposition scheme than the various topological invariants usually used in this context. Most terms appearing in our energy decomposition scheme seem to have simple chemical interpretations. Our observation goes against the well-established knowledge stating that many-body energies are complicated functions of molecular parameters. Our observations might have far-reaching consequences for building accurate machine learning models.
A parametrization scheme for the electronic part of the density-functional based tight-binding (DFTB) method that covers the periodic table is presented. A semiautomatic parametrization scheme has ...been developed that uses Kohn–Sham energies and band structure curvatures of real and fictitious homoatomic crystal structures as reference data. A confinement potential is used to tighten the Kohn–Sham orbitals, which includes two free parameters that are used to optimize the performance of the method. The method is tested on more than 100 systems and shows excellent overall performance.
Sample flow rate is one of the parameters that influence the sensitivity of electrospray ionization (ESI) mass spectrometry. By varying the sample flow rate, initial droplets of different sizes can ...be generated. Protein molecules in small droplets may form gas-phase ions earlier than the ones in large droplets. Here, we have systematically studied the influence of sample flow rate on the ESI charge state distributions (CSDs) of model proteins. A dedicated programmable sample flow rate scanner was used to infuse protein samples at different flow rates into a mass spectrometer. The synergistic influence of sample flow rate and various electrolytes (ammonium acetate, ammonium bicarbonate, ammonium formate, and piperidine) was studied. Significant alterations to the CSDs with increasing flow rate were observed. For example, in the presence of ammonium acetate, at low flow rates, lower charge states of proteins showed high intensities, while at high flow rates, ions related to higher charge states of proteins dominated the spectra. On the other hand, in the presence of piperidine, a significant reduction in the ion currents of all charge states was observed during the flow rate scan. Our observations suggest that at low flow rates the protein molecules follow a charged residue model of ionization mechanism, and at high flow ratesdue to structural changes in protein molecules in large ESI dropletsthe charged residue and chain ejection models can possibly coexist. We propose the use of sample flow rate scan as a way to reveal the influence of flow rate on the CSDs of the studied proteins.
We present a complete set of closed-form formulas for the ZZ polynomials of five classes of composite Kekuléan benzenoids that can be obtained by overlapping two parallelograms: generalized ribbons ...Rb, parallelograms M, vertically overlapping parallelograms MvM, horizontally overlapping parallelograms MhM, and intersecting parallelograms MxM. All formulas have the form of multiple sums over binomial coefficients. Three of the formulas are given with a proof based on the interface theory of benzenoids, while the remaining two formulas are presented as conjectures verified via extensive numerical tests. Both of the conjectured formulas have the form of a 2×2 determinant bearing close structural resemblance to analogous formulas for the number of Kekulé structures derived from the John-Sachs theory of Kekulé structures.
Whether the structure of C
H
X (X = halogen), an intermediate in the halogenation of benzene, is an open or a bridged form has been debated. We produced Br to react with C
H
upon photolysis
of a Br
.../C
H
/
-H
matrix at 3.2 K. In contrast to the C
H
Cl σ-complex reported previously, the observed infrared spectrum indicates that C
H
Br is an open-form π-complex. Furthermore, lines of the two CH out-of-plane bending modes associated mainly with even- and odd-numbered carbons, predicted near 672 and 719 cm
, merged into a broad line at 697.3 cm
, indicating that these modes become nearly equivalent as Br migrates from one carbon atom to another. Quantum-chemical calculations support that the benzene ring performs a bevel-gear-type rotation with respect to Br. Observation of only
-
- and
-
-C
H
Br
suggests that this gear-type motion allows the additional Br atom to attack C
H
Br only from the opposite side of the Br atom in C
H
Br.
Whether the structure of C6H6X (X = halogen), an intermediate in the halogenation of benzene, is an open or a bridged form has been debated. We produced Br to react with C6H6 upon photolysis in situ ...of a Br2/C6H6/p-H2 matrix at 3.2 K. In contrast to the C6H6Cl σ-complex reported previously, the observed infrared spectrum indicates that C6H6Br is an open-form π-complex. Furthermore, lines of the two CH out-of-plane bending modes associated mainly with even- and odd-numbered carbons, predicted near 672 and 719 cm–1, merged into a broad line at 697.3 cm–1, indicating that these modes become nearly equivalent as Br migrates from one carbon atom to another. Quantum-chemical calculations support that the benzene ring performs a bevel-gear-type rotation with respect to Br. Observation of only trans-ortho- and trans-para-C6H6Br2 suggests that this gear-type motion allows the additional Br atom to attack C6H6Br only from the opposite side of the Br atom in C6H6Br.
We present a novel density-functional tight-binding (DFTB) parametrization toolkit developed to optimize the parameters of various DFTB models in a fully automatized fashion. The main features of the ...algorithm, based on the particle swarm optimization technique, are discussed, and a number of initial pilot applications of the developed methodology to molecular and solid systems are presented.
The structures and reactions of pyridine (Pyd) cluster cations in a supersonic molecular beam generated upon photoionization at 9.2–9.4 eV were investigated by infrared (IR) action spectroscopy. The ...mass spectrum showed prominent peaks of (Pyd) m + and H+(Pyd) m , m = 1–5. In the pyridine/pyridine-d 5 mixture, the mass pattern indicated that H+ and D+ migrated during the formation and dissociation of the cluster cations. The IR photodissociation spectra of both (Pyd)2 + and H+(Pyd)2 revealed a N–H stretching band near 3400 cm–1, indicating that their structures are 1-(2-pyridyl)pyridin-1-ium and pyridinium–pyridine, respectively. Observation of the former product implies that the reaction proceeds via an α-distonic cation intermediate, while the latter product is formed via proton migration. The IR spectra of (Pyd) m + and H+(Pyd) m , m ≥ 3, suggested that these clusters consist of a covalently bound (Pyd)2 + or H+(Pyd)2 core, respectively, with additional pyridines attached to them via hydrogen bonds and/or weak dispersive interactions.
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