In search of the dark state of 5-methyl-2-hydroxypyrimidine using a numerical DFT/MRCI gradient

In a recent publication, Lobsiger et al. [Phys. Chem. Chem. Phys. 12, 5032 (2010)] presented infrared and electronic absorption spectra of supersonic jet-cooled 5-methyl-2-hydroxypyrimidine (5M2HP), the enol form of deoxythymine. In addition, they reported on the fast nonradiative decay of the S₁ population to a dark state. In the present paper, we have investigated the mechanism and rate constants of this nonradiative decay by means of quantum chemical multi-configuration methods. To this end, minima of the lowest excited singlet and triplet states as well as the minimum-energy crossing point of singlet and triplet potential energy hypersurfaces (PEHs) have been determined employing a numerical DFT/MRCI gradient where DFT/MRCI stands for a combination of density functional theory (DFT) and a semi-empirical multi-reference configuration interaction (MRCI) approach. Rate constants have been calculated in the Condon approximation using a time-dependent approach based on harmonic oscillator functions and electronic spin–orbit coupling matrix elements evaluated at the DFT/MRCI level. It is shown that the first excited triplet state possesses ³(n?→?π*) character in the gas phase. Fast intersystem crossing is mediated by the low-lying ³(π?→?π*) state whose PEH crosses both, the S₁ ¹(n?→?π*) and T₁ ³(n?→?π*) PEHs.     

1π→1π* Ultraviolet Absorption Bands and Electronic Charge Transfers in Singlet Excited States of Sulfur Aromatic Heterocycles

Abstract

Indoline‐2‐thione (BC), benzimidazole‐2‐thione (BN), benzoxazole‐2‐thione (BO), and benzothiazole‐2‐thione (BS) define an interesting series of aromatic compounds containing a NCS synthonic unit in a heterocyclic ring of five centers, substituted by atomic centers of the type C, N, O, or S, where the main electronic absorption bands are localized in the spectral range of ultraviolet A or B.

The first two singlet electronic transitions of this series, ¹S₀→¹S₁(n,π*) and ¹S₀ → ¹S₂(π,π*), determine the main spectroscopic characteristic of these compounds in order to be used as potential photochemical actinometers of solar ultraviolet radiation. Furthermore, the second electronic transition, localized in the 270–360 nm ultraviolet spectral range, presents a hipsochromic spectral shift as function of the electronic nature of the heteroatomic centers in the heterocyclic ring.

In order to determine a spectroscopic assignment of the main absorption bands in aqueous solution and analyze the effect of the substituent on the electronic charge distributions in the ground and the first two singlet excited electronic states, we have used a semiempirical molecular orbital calculation in the INDO/S‐CIS approach. On the other hand, we have carried out a molecular orbital calculation in the AM1 framework, in order to determine the energetic stability of the thiones with respect to the thiol compounds.     

2,2,9,9‐Tetramethylcyclonona‐3,5,7‐trienylidene vs. its heterocyclic analogues: A quest for stable carbenes at DFT

Replacement of α‐methylenes with BH, AlH, CMe₂, SiH₂, NH, NMe, N^tButyl, NPh, PH, O, and S in non‐planar cyclonona‐3,5,7‐trienylidene (CH₂) alters its status from an unstable transition state to rather stable minima, at B3LYP/6‐311++G**//B3LYP/6‐31 + G* levels of theory. All species appear with singlet closed shell (S_cs) global minima, except for SiH₂ and CH₂ which exhibit triplet electronic ground states. The order of stability based on singlet–triplet energy gap (ΔE_s–t / kcalmol^?1) is: CMe₂ (45.8) > NH (35.8) > NMe (32.3) > O (31.5) > N^tButyl (27.7) ≥ NPh (27.5) ≥ BH (27.4) > S (21.9) > PH (17.0) > CH₂ (?4.4) > SiH₂ (?12.5). In contrast to many reports on N‐heterocyclic carbenes, here alkyl groups appear to exert a higher stabilizing effect than heteroatoms, making CMe₂ the most stable. In addition bulky NMe, N^tButyl, and NPh appear more nucleophilic than their synthesized imidazol‐2‐ylidene congeners. Excluding SiH₂, isodesmic reactions reveal that all substituents stabilize singlet state considerably more than the corresponding triplet. Finally, this work is hoped to pave the path for future matrix isolations and IR studies of these rather stable cyclic non‐planar carbenes. Copyright © 2013 John Wiley & Sons, Ltd.     

Effects of α‐cyclopropyl on heterocyclic carbenes stability at DFT

α‐Cyclopropyl stability impacts on singlet and triplet heterocyclic carbenes with acyclic, cyclic, and cyclic‐unsaturated structures are compared and contrasted to di‐t‐butyl as well as t‐butylcyclopropylcarbenes through appropriate isodesmic reactions at B3LYP/AUG‐cc‐pVTZ level. Substitution of one of the t‐butyl groups of di‐t‐butylcarbene with a cyclopropyl alters the ground state multiplicity from triplet to singlet with a singlet–triplet energy separation (ΔE_s–t) of 7.2 kcal/mol. Additional heteroatom substitution increases ΔE_s–t values for the resulting α‐heteroatom cyclopropylcarbenes in the following order: amino > oxy > thio > phophino. α‐Cyclopropyl group stabilizes singlet states of all our carbenes two to three times more than their corresponding triplet states. The ΔE_s–t values of all the carbenes are increased through cyclization, while the introduction of unsaturation in the rings causes small and rather random changes. To probe the kinetic stability of the species, we calculated the transition states for the opening of cyclopropyl through 1,2‐C shift. Interestingly, the 4.1 kcal/mol energy barrier in cyclopropylcarbene is significantly increased in the presence of heteroatoms to 31.2 kcal/mol for aminocyclopropylcarbene. The reactivity of the species is discussed in terms of nucleophilicity and electrophilicity issues showing our carbenes, especially acyclic ones, more nucleophilic than the common N‐heterocyclic carbenes. Copyright © 2010 John Wiley & Sons, Ltd.     

Computational study of chiral molecules with high intrinsic hyperpolarizabilities

We have investigated the electronic transition, chiroptical properties, and the second-order nonlinear optical (NLO) properties of eight novel chiral diborate compounds and elucidated structure–property relationships from the micromechanism. These compounds show calculated first hyperpolarizabilities (β) ranging from 2738.52 to 83976.45?×?10^?33?esu, which means that subtle structural modifications can substantially enhance the first hyperpolarizability. The cooperativity of intramolecular charge transfer and an effective way to enhance the NLO response were also systemically investigated. The linear correlation between the first hyperpolarizability and the inverse of the electronic transition energy suggests that the electronic transition energy plays a key role in determining the NLO response. These compounds have the potential to be excellent second-order NLO materials from the standpoint of the large β values, high transparency and the intrinsic non-centrosymmetry. The electronic transition and chiroptical properties have been assigned and analysed. The main UV–visible absorption features are best described as π?→?π* transitions. Moreover, the effects of different functionals and basis sets on the first hyperpolarizability were investigated.     

Ylide stabilized carbenes: a computational study

High‐level Density Functional Theory calculations, coupled with appropriate isodesmic reaction, are employed to investigate the effects of α‐carbon, ammonium, phosphorus, and sulfur ylides, cyclization, and unsaturation on the stability, multiplicity, and reactivity of novel singlet (S) and triplet (T) carbenes. Among them the highly π‐donating α‐ammonium ylide is found to exert the highest stabilizing effect on the carbenic center. α‐Ammonium ylides resist dimerization and hydrogenation. They show wider singlet–triplet energy gap (ΔΕ_S–T), broader band gap (ΔΕ_HOMO–LUMO), and higher nucleophilicity compared to the reported stable N‐heterocyclic carbenes. Aromatic cyclic unsaturated ammonium, phosphorus, and sulfur ylide carbenes appear more stable than their saturated cyclic analogs which are in turn more viable than their acyclic counterparts. Copyright © 2014 John Wiley & Sons, Ltd.     

On the nature of some biradicaloid and antiaromatic Vis/NIR‐chromophores

Dyes derived from the biradicalic oxyallyl and cyclopentadienylium were calculated by time‐dependent density functional theory (TDDFT) and the characteristics of the prominent low‐energy transitions revealed by graphical means. According to theoretical and experimental studies, 4‐aminophenyl‐substituted dyes absorb intensely at long wavelengths up to the near infrared. If the amino groups are removed the absorption wavelengths are changed little. As found in the previous studies on the squaraine and croconaine oxyallyl dyes, the substituents play only a minor role in the spectral excitation. Charge‐transfer‐type excitations do not occur between the donor aryl substituents and the central oxyallyl or cyclopentadienylium acceptor group. This behaviour is exceptional since donor–acceptor compounds tend to produce charge‐transfer‐ or polymethine‐type electronic transitions. The hitherto rarely used electron density difference (EDD) maps clearly unveiled the spectral excitation features. The spectral excitation of the title compounds is predominantly localized at the oxyallyl and cyclopentadienylium groups, respectively. Characteristics of simple chromophoric compounds and of conventional CT‐ and polymethine dyes are given for comparison. The biradicaloid character of these dyes is supported by the calculated low singlet–triplet splitting energies. Spin properties were characterized in terms of expectation values of the S²‐operator and antiaromatic properties in terms of nucleus‐independent chemical shifts (NICS). According to the ΔE_S/T and <S²> criteria compounds with the acyclic oxyallyl fragment are more biradicaloid. The parent compounds oxyallyl, thioxyallyl and cyclopentadienylium, display extremely large <S²> values. These compounds are triplets in the ground state. The absorption wavelengths of selected biradicaloid species were also calculated by the multi‐reference SORCI method. Copyright © 2010 John Wiley & Sons, Ltd.     

Theoretical characterisation of highly efficient dye-sensitised solar cells

Molecular electronic structure calculations, employing density functional theory (DFT) and time-dependent density functional theory (TD-DFT) methodologies, have been carried out to improve the performance of the synthesised dye YD2-o-C8 which is characterised by 11.9%–12.7% efficiencies. We aimed to narrow the band gap of YD2-o-C8 to extend the light-harvesting region to near-infrared (NIR). This was done by incorporating Cd instead of Zn onto the porphyrin ring and elongating the length of π-conjugation by adding ethynylene link and anthracene unit, so that the performances of the suggested cells could be expected to exceed the 11.9%–12.7% efficiencies with TiO₂, ZnO₂, and WO₃ oxide electrodes. The effects of modifying the central metal and elongating the length of π-conjugation on cell performance are confirmed in terms of frontier molecular orbital (FMO) energy gaps, density of states (DOS), molecular electrostatic potentials (MEPs), non-linear optical (NLO) properties, ultraviolet–visible (UV–vis) electronic absorption, and ¹H nuclear magnetic resonance chemical shifts. Increasing the length of π-conjugation of the D–π–A dyes leads to increasing the DOS near Fermi levels, more active NLO performance, strong response to the external electric field, delocalisation of the negative charges near the anchoring groups, deep electron injection, suppressing macrocycle aggregation, active dye regeneration, and inhibited dye recombination. The calculated band gap/eV of the present DMP-Zn is correlated with the experimental (E_1/2(oxidation)–E_1/2(reduction)/V) potentials of the identical YD2-o-C8. A co-sensitiser is suggested for NIR sensitisation (550–950 nm) to increase the power-to-conversion efficiency beyond 14%.     

Electronic and spectral properties of ametal-organic super container molecule by single point DFT

ABSTRACT

Metal-organic super container (MOSC) molecules are ideal candidates for photocatalysis due to their construction with transition metal centres and tuneable cavity sizes that could house catalytic sites. The basic electronic structure for a model of extremely large size (more than 2000 ions) is explored by single point calculation using unrestricted density functional theory, and Perdue–Burke–Ernzerhof functional in Vienna ab initio simulation package software. The information obtained through these calculations (such as density of states, absorbance spectra, and charge density) will allow for analysis of a MOSC's catalytic ability. Electronic characteristics of the nanostructures (MOSCs and their building blocks) in the ground and photoexcited electronic configurations are examined. We explore if the presence of transition metal ions with open shells in such close proximity to one another may result in high spin configurations and show any arrangement into ferromagnetic ordering. Spin-unrestricted computation was applied to evaluate how optical properties could be affected by d–d transitions. A scan of a spin-polarisation parameter allows one to resolve spin configuration and obtain a connection between theory and experiment. Analysis of Kohn–Sham orbitals of interest provides insight into charge transfer mechanisms, which were found to contribute to multiple low-energy charge transfer states to the electronic structure.     

Does gold cluster promote or scavenge radicals? A controversy at DFT

Anticancer character of gold cluster has been indicated through its free radical scavenging properties. This is in contrast to its free radical promoting ability suggested by other workers. Here, we address this controversy by probing the stabilizing effects of Au₃ cluster on RO^? vs its impacts on RO–H bond dissociation enthalpy, at B3LYP/ LACVP+* level (R═H, methyl, ethyl, n‐propyl, i‐propyl, n‐butyl, t‐butyl, and phenyl). In the presence of Au₃ cluster, bond dissociation enthalpy of O–H bond and the spin density at the RO^? oxygen are reduced dramatically. These are clear evidences for both the Au₃ facilitation of the RO–H bond breakage and its scavenging of RO^? radical. Since O–Au anchoring bond is responsible for the interaction of Au₃ cluster and ROH (or RO^?), its nature was interpreted by means of the quantum theory of atoms in molecules and the natural bond orbital. The results indicate that O–Au bond is stronger and has more covalent character in RO^?–Au₃ than in ROH–Au₃. The interaction of Au₃ cluster with RO^? is 1.5 to 3 times more than that with ROH. As a result, gold cluster scavenging property appears more prominent than its free radical initiation activity.     

DFT study of the biphenylene–NO complexes formed in nitration mechanism

The most probable complexes formed in biphenylene (BP) nitration pathway have been investigated at B3LYP/6‐31+G(d,p) level of theory in the gas phase. To obtain more accurate energies, single point calculations were carried out at B3LYP/6‐31++G(2d,2p), B3PW91/6‐31+G(d,p), and B3PW91/6‐31++G(2d,2p) levels using B3LYP/6‐31+G(d,p) optimized geometry. The six intermediates and one transition state were found before the subsequent formation of the arenium ion on the potential energy surface of the electrophilic nitration of BP. It was also shown that the position β in the BP is much more susceptible to electrophilic attack than the competing position α. The Natural Bond Orbital (NBO), Charges from Electrostatic Potentials using a Grid based method (CHelpG), and Merz–Singh–Kollman (MK) charges and s‐characters of atoms involved in the reaction mechanism were calculated. Inspection of charges in the moieties indicates that the positive charge in all complexes is chiefly located on the BP, which means that theNO₂ moiety received the electron from the BP. To investigate the nature of BP– interaction in the five π‐complexes, atoms in molecules (AIM) analysis was performed. The AIM results suggested that the BP– interactions have an electrostatic characteristic. In addition, high electrostatic interactions were predicted in π‐complexes in which one of the oxygen atoms of interacts with the BP. Nucleus‐independent chemical shift (NICS) methodology has been applied to study the change of antiaromaticity in four‐membered ring of BP upon complexation with . The results based on NICS calculations show that antiaromaticity of four‐membered ring decreases upon complexation. Copyright © 2008 John Wiley & Sons, Ltd.     

Structural and Electronic (Absorption and Fluorescence) Properties of a Stable Triplet Diphenylcarbene: A DFT Study

A triplet diphenylcarbene, bis[3-bromo-5-(trifluoromethyl)[1,1'-biphenyl]-4-yl]methylidene (B3B), with exceptional stability was discovered by chemists from Japan's Mie University. To investigate its different quantum chemical features, a theoretical analysis was predicated on Density Functional Theory (DFT) and Time Dependent-DFT (TD-DFT) based technique. According to the findings, the singlet–triplet energy gap (ES-T), as well as HOMO–LUMO energy bandgap (E_H-L), was found to be diminished when nucleophilicity (N) rose. We looked at the geometrical dimensions, molecular orbitals (MOs), electronic spectra, electrostatic potential, molecular surfaces, reactivity characteristics, and thermodynamics features of the title carbene (B3B). Its electronic spectra in different solvents were calculated using TD-DFT and Polarizable Continuum Model (PCM) framework. The estimated absorption maxima of B3B were seen between 327 and 340 nm, relying on the solvents, and were attributed to the S⁰?→?S¹ transition. Estimated fluorescence spectral peaks were found around 389 and 407 nm with the S¹ and S⁰ transitions being identified. Its fluorescence/absorption intensities revealed a blue shift change when the solvent polarity was increased. The least exciting state has been discovered to be the π?→?π^* charge-transfer (CT) phase. According to the Natural Bonding Orbital (NBO) exploration, ICT offers a significant role in chemical system destabilization. Furthermore, several hybrid features were used to determine the NLO (nonlinear optical) features (polarizability, first-order hyperpolarizability, and dipole moment). The calculated values suggest that B3B is a promising candidate for further research into nonlinear optical properties.

Graphical Abstract

     

Involvement of weak C?H···X hydrogen bonds in metal‐to‐semiconductor regime change in one‐dimensional organic conductors (o‐DMTTF)2X (X = Cl,Br, and I): combined IR and Raman studies

We report on the infrared (IR) and Raman studies of the three isostructural quasi‐one‐dimensional cation radical salts of 3,4‐dimethyl‐tetrathiafulvalene (o‐DMTTF)₂X (X = Cl, Br, and I), which all exhibit metallic properties at room temperature and undergo transitions to a semiconducting state in two steps: a soft metal‐to‐semiconductor regime change in the temperature region T_ρ = 5–200 K and then a sharp phase transition at about T_MI = 50 K. Polarized IR reflectance spectra (700–16 000 cm⁻¹) and Raman spectra (50–3500 cm⁻¹, excitation λ = 632.8 nm) of single crystals were measured as a function of temperature (T = 5–300 K) to assess the eventual formation of a charge‐ordered state below 50 K. Additionally, the temperature dependence of the IR absorption spectra of powdered crystals in KBr discs was also studied. The Raman spectra and especially the bands related to the CC stretching vibration of o‐DMTTF provide unambiguous evidence of uniform charge distribution on o‐DMTTF down to the lowest temperatures, without any modification below 50 K. However, the temperature dependence of Raman spectra indicates a regime change below about 200 K. Temperature dependence of both electronic dispersion and vibrational features observed in the IR spectra also clearly confirms the regime change below about 200 K and shows the involvement of C H···X hydrogen bonds in the electronic localization; some spectral changes can be also related with the phase transition at 50 K. Additionally, using density functional theory methods, the normal vibrational modes of the neutral o‐DMTTF⁰ and cationic o‐DMTTF⁺ species, as well as their theoretical IR and Raman spectra, were calculated. The theoretical data were compared with the experimental IR and Raman spectra of neutral o‐DMTTF molecule. Copyright © 2011 John Wiley & Sons, Ltd.     

Reaching for [6]n SiC‐cyclacenes and [6]n SiC‐acenes: A DFT approach

Density functional theory (DFT) calculations introduced triplet ground states for [6]_n SiC‐cyclacenes and ‐acenes with alternate silabenzene rings including silicon atoms in 2 opposite edges (n = 6, 8, 10, 12). The singlet‐triplet energy gap (ΔE_(S‐T)), binding energy per atom (BE/n), and NBO calculation with very small band gap (ΔE_LUMO‐HOMO) confirmed the triplet ground states. In contrast to polyacenes, the singlet [6]_n SiC‐cyclacenes displayed more stability improvement than triplets, through n increasing. This may open the way for synthesis of larger stable [6]_n SiC‐cyclacenes. The ΔE_(S‐T), BE/n, and the strain energy through homodesmic equations indicated more stability for larger [6]_n SiC‐cyclacenes, which was more noticeable in singlet states. Cyclacenes and acenes with high conductivity and full point charge were introduced as suitable candidates for hydrogen storage.     

NLO characteristics of D-π-A coumarin-thiophene bridged azo dyes by Z-scan and DFT methods

ABSTRACT

The structural, electronic, intramolecular charge transfer (ICT) and nonlinear optical (NLO) properties of the donor-π-acceptor (D-π-A) azo linked dyes bearing coumarin thiophene bridge with different acceptors were inspected by Z-scan and DFT methods. The dye 3a exhibits bathochromic absorption maxima (649 and 650?nm) in the near IR region in DMF and DMSO. The dye 3a holds low HOMO–LUMO gap elucidated by CV and DFT indicating strong ICT character. The thermal stability is high for 3a and it shows enhanced NLO property by Z-scan and DFT methods as predicted in both global and range-separated hybrid functionals. The molecular geometry was optimised using B3LYP/6-311?+?g(d,p). The ICT characteristics are correlated with NLO properties obtained by Z-scan and DFT techniques.     

Solvatochromism as an efficient tool to study N,N‐dimethylamino‐ and cyano‐substituted π‐conjugated molecules with an intramolecular charge‐transfer absorption

A representative data set has been gained by the measurement of the electronic absorption spectra of 12 systematically selected push–pull systems with an intramolecular charge‐transfer (CT) absorption and the general structure D–π–A (D = donor, A = acceptor) featuring electron‐withdrawing CN groups, electron‐donating N(CH₃)₂ groups, and various π‐conjugated backbones in 32 solvents with different polarities. The longest‐wavelength absorption maxima λ_max and the corresponding wavenumbers $\tilde {v}_{{\rm max}} $ were evaluated from the UV/Vis spectra measured in 32 well‐selected solvents. The D–π–A push–pull systems were further characterized by quantum‐chemical quantities and simple structural parameters. Structure–solvatochromism relationships were evaluated by multidimensional statistic methods. Whereas solvent polarizability and solvent cavity size proved to be the most important factors affecting the position of λ_max, the solvent polarity was less important. The most important characteristics of organic CT compounds are the energy of the LUMO, the permanent dipole moment, the COSMO (COnductor‐like Screening MOdel) area, the COSMO volume, the number, and ratio of N,N‐dimethylamino and cyano groups, and eventually the number of triple bonds (π‐linkers). A relation between the first‐order polarizability α, the longest‐wavelength absorption maxima λ_max, and the structural features has also been found. The higher‐order polarizabilities β and γ are not related to the observed solvatochromism. Copyright © 2010 John Wiley & Sons, Ltd.     

Comparison of SERRS and RRS excitation profiles of [Fe(tpy)2]2+ (tpy = 2,2':6',2'‐terpyridine) supported by DFT calculations: effect of the electrostatic bonding to chloride‐modified Ag nanoparticles on its vibrational and electronic structure

Nonresonance (or normal) Raman scattering (NRS), resonance Raman scattering (RRS), surface‐enhanced Raman scattering (SERS), and surface‐enhanced RRS (SERRS) spectra of [Fe(tpy)₂]²⁺ complex dication (tpy = 2,2':6',2''‐terpyridine) are reported. The comparison of RRS/NRS and SERRS/SERS excitation profiles of [Fe(tpy)₂]²⁺ spectral bands in the range of 445–780 nm is supported by density functional theory (DFT) calculations, Raman depolarization measurements, comparison of the solid [Fe(tpy)₂](SO₄)₂ and solution RRS spectra, and characterization of the Ag nanoparticle (NP) hydrosol/[Fe(tpy)₂]²⁺ SERS/SERRS active system by surface plasmon extinction spectrum and transmission electron microscopy image of the fractal aggregates (D = 1.82). By DFT calculations, both the Raman active modes and the electronic states of the complex have been assigned to the symmetry species of the D_2d point group. It has been demonstrated that upon the electrostatic bonding of the complex dication to the chloride‐modified Ag NPs, the geometric and ground state electronic structure of the complex and the identity of the three different metal‐to‐ligand charge transfer (¹MLCT) electronic transitions remain preserved. On the other hand, the effect of ion pairing manifests itself by a slight change in localization of one of the electronic transitions (with max. at 552 nm) as well as by promotion of the Herzberg–Teller activation of E modes resulting from coupling of E and B₂ excited electronic states. Finally, the very low, 1 × 10⁻¹¹ M SERRS spectral detection limit of [Fe(tpy)₂]²⁺ at 532‐nm excitation is attributed to a concerted action of the electromagnetic and molecular resonance mechanism, in conjunction to the electrostatic bonding of the complex dication to the chloride‐modified Ag NP surface. Copyright © 2014 John Wiley & Sons, Ltd.     

Two-photon vibronic spectroscopy of allene at 7.0–10.5 eV: experiment and theory

2?+?1 resonance-enhanced multiphoton ionization (REMPI) spectra of allene at 7.0–10.5?eV have been observed. The excited vibronic symmetry has been determined from polarization-ratio measurements. Based on the vibronic energies and peak intensities calculated using ab initio MO and time-dependent density functional theory, the very congested REMPI spectra have been assigned as due to π*?←?π, 3p?←?π, 4s?←?π, 4p?←?π, and 4d?←?π transitions. Vibrational progressions related to the CH₂ twisting (ν₄ ～770?cm^?1) have been observed for several excited electronic states. Calculated Franck–Condon factors also confirm that CH₂ twisting is the most active mode in the vibronic spectra of allene. In this study, theoretical calculations of two-photon intensities and polarization ratios have been made through the ab initio computed one-photon transition dipole moments to various electronic states as intermediates. As a starting point to interpret the complicated vibronic spectrum of allene, the theoretical approach, without vibronic couplings, has been applied to predict the peak positions, spectral intensities, and polarization ratios of Rydberg states, and qualitatively shows a considerable agreement with experimental observations.     

Substituent effects on cyclonona‐3,5,7‐trienylidenes: a quest for stable carbenes at density functional theory level

Nine boat‐shaped cyclonona‐3,5,7‐trienylidenes are compared and contrasted with respect to their multiplicity, nucleophilicity, electrophilicity, band gap (ΔE_{HOMO ? LUMO}), Natural bond orbital (NBO) atomic charge, force constant, as well as the aptitude for dimerization, and rearrangement through proper isodesmic reactions at B3LYP/AUG‐cc‐pVTZ and B3LYP/6‐311++G**//B3LYP/6‐31+G* levels of theory. The nine cyclic carbenes include unsubstituted (1_CH2) plus eight α‐cyclopropylcyclonona‐3,5,7‐trienylidenes, which are substituted with ?‐SiMe₂, ?‐NMe, ?‐PMe, ?‐O, ?‐S, ?‐CH₂, ?‐cyclopropyl, and ?‐CMe₂ (2_SiMe2, 2_NMe, 2_PMe, 2_O, 2_S, 2_CH2, 2_cyclopropyl, and 2_CMe2, respectively). The latter eight species enjoy the stabilizing interaction of the occupied Walsh orbital of cyclopropyl with the vacant p_π orbital of the carbene center (Walsh_cyclopropyl → p_{π carbene}). Among them, the singlet closed shell 2_NMe appears the most promising for exhibiting the highest relative singlet–triplet energy gap (ΔE_{s ? t} = 27.1 kcal mol^?1). In contrast, the least stable derivative is triplet 2_SiMe2, which exhibits the lowest relative ΔE_{s ? t} of ?5.5 kcal mol^?1. The overall trend of ΔE_s‐t is 2_NMe > 2_PMe > 2_S > 2_O > 2_cyclopropyl > 2_CMe2 > 2_CH2 > 1_CH2 > 2_SiMe2. With one negative force constant, the unsubstituted 1_CH2 turns out to be a transition state, whereas the rest emerge as minima. Copyright © 2015 John Wiley & Sons, Ltd.     

The Skyrme model with a U*(1) gauged Wess‐Zumino term in a noncommutative spacetime

The Skyrme model is generalized for a noncommutative spacetime with the Weyl‐operators of SU(2) matrices and the corresponding star‐product. The unitary condition and the topological current can be extended to star‐exponential matrices. The Wess‐Zumino term which breaks unphysical symmetries of the Skyrme action is gauged with the U_*(1) group to allow for electromagnetic processes in a noncommutative spacetime. Apart from corrections to the anomalous decay γ→π⁰π⁺π^– in commuting spacetime, the additional anomalous process γ→π⁰π⁰π⁰ is found in the U_*(1) gauged Wess‐Zumino action for a noncommutative spacetime.