Br2 elimination in 248-nm photolysis of CF2Br2 probed by using cavity ring-down absorption spectroscopy

By using cavity ring-down absorption spectroscopy technique, we have observed the channel of Br2 molecular elimination following photodissociation of CF2Br2 at 248 nm. A tunable laser beam, which is crossed perpendicular to the photolyzing laser beam in a ring-down cell, is used to probe the Br2 fragment in the B 3Piou+-X1Sigmag+ transition. The vibrational population is obtained in a nascent state, despite ring-down time as long as 500-1000 ns. The population ratio of Br2(v=1)/Br2(v=0) is determined to be 0.4+/-0.2, slightly larger than the value of 0.22 evaluated by Boltzmann distribution at room temperature. The quantum yield of the Br2 elimination reaction is also measured to be 0.04+/-0.01. This work provides direct evidence to support molecular elimination occurring in the CF2Br2 photodissociation and proposes a plausible pathway with the aid of ab initio potential-energy calculations. CF2Br2 is excited probably to the 1B1 and 3B2 states at 248 nm. As the C-Br bond is elongated upon excitation, the coupling of the 1A'(1B1) state to the high vibrational levels of the ground state X 1A'(1A1) may be enhanced to facilitate the process of internal conversion. After transition, the highly vibrationally excited CF2Br2 feasibly surpasses a transition barrier prior to decomposition. According to the ab initio calculations, the transition state structure tends to correlate with the intermediate state CF2Br+Br(CF2Br...Br) and the products CF2+Br2. A sequential photodissociation pathway is thus favored. That is, a single C-Br bond breaks, and then the free-Br atom moves to form a Br-Br bond, followed by the Br2 elimination. The formed Br-Br bond distance in the transition state tends to approach equilibrium such that the Br2 fragment may be populated in cold vibrational distribution. Observation of a small vibrational population ratio of Br2(v=1)Br2(v=0) agrees with the proposed mechanism.     

Coupled-cluster studies of the lowest excited states of the 11-cis-retinal chromophore

The first few excited states of the 11-cis-retinal (PSB11) chromophore have been studied at the coupled-cluster approximative singles and doubles (CC2) level using triple-zeta quality basis sets augmented with double sets of polarisation functions. The two lowest vertical excitation energies of 2.14 and 3.21 eV are in good agreement with recently reported experimental values of 2.03 and 3.18 eV obtained in molecular beam measurements. Calculations at the time-dependent density functional theory (TDDFT) level using the B3LYP hybrid functional yield vertical excitation energies of 2.34 and 3.10 eV for the two lowest states. Zero-point vibrational energy (ZPVE) corrections of -0.09 and -0.17 eV were deduced from the harmonic vibrational frequencies for the ground and excited states calculated at the density functional theory (DFT) and TDDFT level, respectively, using the B3LYP hybrid functional.     

Structural and electronic properties of polyacetylene and polyyne from hybrid and Coulomb-attenuated density functionals

The bond length alternation (BLA), the highest-occupied-lowest-unoccupied (HO-LU) orbital energy gap, and the corresponding excitation energy are determined for trans-polyacetylene (PA) and polyyne (PY) using density functional theory. Results from the Coulomb-attenuated CAM-B3LYP functional are compared with those from the conventional BHHLYP and B3LYP hybrid functionals. BLA values and HO-LU gaps are determined using both finite oligomer and infinite chain calculations, subject to periodic boundary conditions. TDDFT excitation energies are determined for the oligomers. The oligomer excitation energies and HO-LU gaps are then used, in conjunction with the infinite chain HO-LU gap, to estimate the infinite chain excitation energy. Overall, BHHLYP and CAM-B3LYP give BLA values and excitation energies that are larger and more accurate than those obtained using B3LYP. The results highlight the degree to which excitation energies can be approximated using the HO-LU gaps-at the infinite limit, this approximation works well for B3LYP, but not for the other functionals, where the HO-LU gap is significantly larger. The study provides further evidence for the high-quality theoretical predictions that can be obtained from the CAM-B3LYP functional.     

Relationship between orbital energy gaps and excitation energies for long‐chain systems

The difference between the excitation energies and corresponding orbital energy gaps, the exciton binding energy, is investigated based on time‐dependent (TD) density functional theory (DFT) for long‐chain systems: all‐trans polyacetylenes and linear oligoacenes. The optimized geometries of these systems indicate that bond length alternations significantly depend on long‐range exchange interactions. In TDDFT formalism, the exciton binding energy comes from the two‐electron interactions between occupied and unoccupied orbitals through the Coulomb‐exchange‐correlation integral kernels. TDDFT calculations show that the exciton binding energy is significant when long‐range exchange interactions are involved. Spin‐flip (SF) TDDFT calculations are then carried out to clarify double‐excitation effects in these excitation energies. The calculated SF‐TDDFT results indicate that double‐excitation effects significantly contribute to the excitations of long‐chain systems. The discrepancies between the vertical ionization potential minus electron affinity (IP–EA) values and the HOMO–LUMO excitation energies are also evaluated for the infinitely long polyacetylene and oligoacene using the least‐square fits to estimate the exciton binding energy of infinitely long systems. It is found that long‐range exchange interactions are required to give the exciton binding energy of the infinitely long systems. Consequently, it is concluded that long‐range exchange interactions neglected in many DFT calculations play a crucial role in the exciton binding energies of long‐chain systems, while double‐excitation correlation effects are also significant to hold the energy balance of the excitations. © 2016 Wiley Periodicals, Inc.     

Performance of the M11 and M11-L density functionals for calculations of electronic excitation energies by adiabatic time-dependent density functional theory

Adiabatic time-dependent density functional theory is a powerful method for calculating electronic excitation energies of complex systems, but the quality of the results depends on the choice of approximate density functional. In this article we test two promising new density functionals, M11 and M11-L, against databases of 214 diverse electronic excitation energies, and we compare the results to those for 16 other density functionals of various kinds and to time-dependent Hartree-Fock. Charge transfer excitations are well known to be the hardest challenge for TDDFT. M11 is a long-range-corrected hybrid meta-GGA, and it shows better performance for charge transfer excitations than any of the other functionals except M06-HF, which is a specialized functional that does not do well for valence excitations. Several other long-range-corrected hybrid functionals also do well, and we especially recommend M11, ωB97X, and M06-2X for general spectroscopic applications because they do exceptionally well on ground-state properties as well as excitation energies. Local functionals are preferred for many applications to extended systems because of their significant cost advantage for large systems. M11-L is a dual-range local functional and-unlike all previous local functionals-it has good performance for Rydberg states as well as for valence states. Thus it is highly recommended for excitation energy calculations on extended systems.     

On low‐lying excited states of extended nanographenes

Low‐lying excited states of planarly extended nanographenes are investigated using the long‐range corrected (LC) density functional theory (DFT) and the spin‐flip (SF) time‐dependent density functional theory (TDDFT) by exploring the long‐range exchange and double‐excitation correlation effects on the excitation energies, band gaps, and exciton binding energies. Optimizing the geometries of the nanographenes indicates that the long‐range exchange interaction significantly improves the C C bond lengths and amplify their bond length alternations with overall shortening the bond lengths. The calculated TDDFT excitation energies show that long‐range exchange interaction is crucial to provide accurate excitation energies of small nanographenes and dominate the exciton binding energies in the excited states of nanographenes. It is, however, also found that the present long‐range correction may cause the overestimation of the excitation energy for the infinitely wide graphene due to the discrepancy between the calculated band gaps and vertical ionization potential (IP) minus electron affinity (EA) values. Contrasting to the long‐range exchange effects, the SF‐TDDFT calculations show that the double‐excitation correlation effects are negligible in the low‐lying excitations of nanographenes, although this effect is large in the lowest excitation of benzene molecule. It is, therefore, concluded that long‐range exchange interactions should be incorporated in TDDFT calculations to quantitatively investigate the excited states of graphenes, although TDDFT using a present LC functional may provide a considerable excitation energy for the infinitely wide graphene mainly due to the discrepancy between the calculated band gaps and IP–EA values. © 2017 Wiley Periodicals, Inc.     

The relative energies of polypeptide conformers predicted by linear scaling second-order Møller-Plesset perturbation theory

We describe an implementation of the cluster-in-molecule(CIM) resolution of the identity(RI) approximation second-order M?ller–Plesset perturbation theory(CIM-RI-MP2), with the purpose of extending RI-MP2 calculations to very large systems. For typical conformers of several large polypeptides, we calculated their conformational energy differences with the CIM-RI-MP2 and the generalized energy-based fragmentation MP2(GEBF-MP2) methods, and compared these results with the density functional theory(DFT) results obtained with several popular functionals. Our calculations show that the conformational energy differences obtained with CIM-RI-MP2 and GEBF-MP2 are very close to each other. In comparison with the GEBF-MP2 and CIM-RI-MP2 relative energies, we found that the DFT functionals(CAM-B3LYP-D3, LC-?PBE-D3, M05-2X, M06-2X and ?B97XD) can give quite accurate conformational energy differences for structurally similar conformers, but provide less-accurate results for structurally very different conformers.     

QM/MM study of the absorption spectra of DsRed.M1 chromophores

We report geometries and vertical excitation energies for the red and green chromophores of the DsRed.M1 protein in the gas phase and in the solvated protein environment. Geometries are optimized using density functional theory (DFT, B3LYP functional) for the isolated chromophores and combined quantum mechanical/molecular mechanical (QM/MM) methods for the protein (B3LYP/MM). Vertical excitation energies are computed using DFT/MRCI, OM2/MRCI, and TDDFT as QM methods. In the case of the red chromophore, there is a general blue shift in the excitation energies when going from the isolated chromophore to the protein, which is caused both by structural changes and by electrostatic interactions with the environment. For the lowest ππ* transition, these two factors contribute to a similar extent to the overall DFT/MRCI shift of 0.4 eV. An enlargement of the QM region to include active‐site residues does not change the DFT/MRCI excitation energies much. The DFT/MRCI results are closest to experiment for both chromophores. OM2/MRCI and TDDFT overestimate the first vertical excitation energy by 0.3–0.5 and 0.2–0.4 eV, respectively, relative to the experimental or DFT/MRCI values. The experimental gap of 0.35 eV between the lowest ππ* excitation energies of the red (cis‐acylimine) and green (trans‐peptide) forms is well reproduced by DFT/MRCI and TDDFT (0.32 and 0.37 eV, respectively). A histogram spectrum for an equal mixture of the two forms, generated by OM2/MRCI calculations on 450 snapshots along molecular dynamics trajectories, matches the experimental spectrum quite well, with a gap of 0.23 eV and an overall blue shift of about 0.3 eV. DFT/MRCI appears as an attractive choice for calculating excitation energies in fluorescent proteins, without the shortcomings of TDDFT and computationally more affordable than CASSCF‐based approaches. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

A semiempirical long-range corrected exchange correlation functional including a short-range Gaussian attenuation (LCgau-B97)

We applied an improved long‐range correction scheme including a short‐range Gaussian attenuation (LCgau) to the Becke97 (B97) exchange correlation functional. In the optimization of LCgau‐B97 functional, the linear parameters are determined by least squares fitting. Optimizing μ parameter (0.2) that controls long‐range portion of Hartree‐Fock (HF) exchange to excitation energies of large molecules (Chai and Head‐Gordon, J Chem Phys 2008, 128, 084106) and additional short‐range Gaussian parameters (a = 0.15 and k = 0.9) that controls HF exchange inclusion ranging from short‐range to mid‐range (0.5–3 Å) to ground state properties achieved high performances of LCgau‐B97 simultaneously on both ground state and excited state properties, which is better than other tested semiempirical density functional theory (DFT) functionals, such as ωB97, ωB97X, BMK, and M0x‐family. We also found that while a small μ value (～0.2) in LC‐DFT is appropriate to the local excitation and intramolecular charge‐transfer excitation energies, a larger μ value (0.42) is desirable in the Rydberg excitation‐energy calculations. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011     

A Quantum Chemical Study of the Ground and Excited State Electronic Structures of Carbazole Oligomers with and without Triarylborane Substitutes

Recent experimental investigation (Reitzenstein and Lambert,Macromolecules, 2009, 42, 773) indicated that the quite different optical properties of 2,7- and 3,6-linkage triarylboryl carbazole oligomers may arise from the different nature of their low-lying excited states: a low-lying delocalized within-backbone excitation in longer 2,7-linked oligomers vs a backbone-to-sidechain charge-transfer (CT) excitation independent of the polymerization length in 3,6-linked oligomers. Here in this paper, two long-range corrected functionals, CAM-B3LYP and ωB97X, are applied together with the traditional B3LYP functional in time-dependent density functional theory (TDDFT) calculations to systematically investigate the low-lying electronic excitations in both oligomers. Our calculations indicate that an extensive conjugation exists between monomer molecular orbitals in 2,7-linked oligomers, which is absent in those of 3,6-linked structures, resulting in a considerable narrowing of the HOMO-LUMO gap of their backbone moiety, while having little effect on the side-chains. CAM-B3LYP and ωB97x calculations confirm that the lowest-energy absorption is a within-backbone excitation in longer 2,7-linked oligomers as opposed to a backbone to side-chain charge transfer excitation in 2,7-linked oligmers of shorter length and 3,6-linked oligomers of any length. All these findings are consistent with the experimental findings and the qualitative energy diagram proposed by Reitzenstein and Lambert.     

Spin-orbit density functional and ab initio study of HgX(n) (X=F, Cl, Br, and I; n=1, 2, and 4)

Quantum chemical calculations of HgX(n) (X=F, Cl, Br, and I; n=1, 2, and 4) in the gas phase are performed using the density functional theory (DFT), two-component spin-orbit (SO) DFT, and high-level ab initio method with relativistic effective core potentials (RECPs). Molecular geometries, vibrational frequencies, and various thermochemical energies are calculated and compared with available experimental results. We assess the performances of DFT functionals for calculating various molecular properties. The PBE0 functional is generally reasonable for the molecular geometries and the vibrational frequencies, but the M06 functional is more appropriate for estimating thermochemical energies. Both shape-consistent and energy-consistent RECPs correctly describe the SO effect.     

HF and DFT studies of the structure and vibrational spectra of 8-hydroxyquinoline and its mercury(II) halide complexes

The geometry, frequency and intensity of the vibrational bands of 8-hydroxyquinoline (8-HOQ) were obtained by HF and density functional theory (DFT) with BLYP and B3LYP functionals and 6-31G(d) as the basis set. The optimized bond lengths and bond angles are in good agreement with the X-ray data. The vibrational spectra of 8-HOQ which is calculated by the HF and DFT methods, reproduces the vibrational wavenumbers and intensities with an accuracy, which allows reliable vibrational assignments. Complexes of the type Hg(8-HOQ)X(2) [where X = Cl , Br] have been studied in the 4000-200 cm(-1) region, and assignment of all the observed bands were made. The analysis of the infrared spectra indicates that there are some structure-spectra correlations.     

Description of core excitations by time-dependent density functional theory with local density approximation, generalized gradient approximation, meta-generalized gradient approximation, and hybrid functionals

Time-dependent density functional theory (TDDFT) is employed to investigate exchange-correlation-functional dependence of the vertical core-excitation energies of several molecules including H, C, N, O, and F atoms. For the local density approximation (LDA), generalized gradient approximation (GGA), and meta-GGA, the calculated X1s-->pi* excitation energies (X = C, N, O, and F) are severely underestimated by more than 13 eV. On the other hand, time-dependent Hartree-Fock (TDHF) overestimates the excitation energies by more than 6 eV. The hybrid functionals perform better than pure TDDFT because HF exchange remedies the underestimation of pure TDDFT. Among these hybrid functionals, the Becke-Half-and-Half-Lee-Yang-Parr (BHHLYP) functional including 50% HF exchange provides the smallest error for core excitations. We have also discovered the systematic trend that the deviations of TDHF and TDDFT with the LDA, GGA, and meta-GGA functionals show a strong atom-dependence. Namely, their deviations become larger for heavier atoms, while the hybrid functionals are significantly less atom-dependent.     

卤素氮氧化物的结构和光谱性质的理论研究

通过DFT/B3LYP计算,优化了卤素氮氧化物XNO_2及其异构体XONO（X = F,Cl ,Br,I）的平衡几何构型,预测了异构体的相对稳定性及其相互转化的活化能垒 。在B3LYP和QCISD（T）计算水平上,确定了X-NO_2键的解离能。应用与时间有关 的密度泛函理论（TD-B3LYP）计算了XNO_2低激发态的跃迁能,并讨论了这些激发 态与卤素氮氧化物光诱导解离过程的关联。     

A long-range-corrected time-dependent density functional theory

We apply the long-range correction (LC) scheme for exchange functionals of density functional theory to time-dependent density functional theory (TDDFT) and examine its efficiency in dealing with the serious problems of TDDFT, i.e., the underestimations of Rydberg excitation energies, oscillator strengths, and charge-transfer excitation energies. By calculating vertical excitation energies of typical molecules, it was found that LC-TDDFT gives accurate excitation energies, within an error of 0.5 eV, and reasonable oscillator strengths, while TDDFT employing a pure functional provides 1.5 eV lower excitation energies and two orders of magnitude lower oscillator strengths for the Rydberg excitations. It was also found that LC-TDDFT clearly reproduces the correct asymptotic behavior of the charge-transfer excitation energy of ethylene-tetrafluoroethylene dimer for the long intramolecular distance, unlike a conventional far-nucleus asymptotic correction scheme. It is, therefore, presumed that poor TDDFT results for pure functionals may be due to their lack of a long-range orbital-orbital interaction.     

FT-IR spectra, vibrational assignments, and density functional calculations of imidazo[1,2-a]pyridine molecule and its Zn(II) halide complexes

The geometry, frequency, and intensity of the vibrational bands of imidazo[1,2-a]pyridine (which is abbreviated as impy) were obtained by the density functional theory (DFT) calculations with BLYP, B3LYP, and B3PW91 functionals and 6-31G(d) basis set. The optimized geometric bond lengths and bond angles are in good agreement with the available X-ray data. The infrared spectrum of imidazo[1,2-a]pyridine was computed by the DFT method in order to reproduce the vibrational wavenumbers and intensities with an accuracy, which allows reliable vibrational assignments. Total energy distribution and isotopic shifts have been calculated in order to help for the perfect assignment of the vibrational modes. The zinc halide complexes Zn(impy)₂X₂ [X = Cl, Br, and I] have also been synthesized. The compounds were characterized using the elemental analysis, FT-IR spectra, and quantum chemical calculations. The geometry optimization of Zn(impy)₂X₂ yields distorted tetrahedral environment around Zn ion.     

Four-dimensional quantum study on exothermic complex-forming reactions: Cl- + CH3Br-->ClCH3+Br-

The exothermic gas-phase bimolecular nucleophilic substitution (S(N)2) reaction Cl(-)+CH(3)Br (upsilon1',upsilon2',upsilon3')-->ClCH(3) (upsilon1,upsilon2,upsilon3)+Br- and the corresponding endothermic reverse reaction have been studied by time-independent quantum scattering calculations in hyperspherical coordinates on a coupled-cluster potential-energy surface. The dimensionality-reduced model takes four degrees of freedom into account [Cl-C and C-Br stretching modes (quantum numbers upsilon3' and upsilon3); totally symmetric modes of the methyl group, i.e., C-H stretching (upsilon1' and upsilon1) and umbrella bending vibrations (upsilon2' and upsilon2)]. Diagonalization of the Hamiltonian was performed employing the Lanczos algorithm with a variation of partial reorthogonalization. A narrow grid in the total energy was employed so that long-living resonance states could be resolved and extracted. While excitation of the reactant umbrella bending mode already leads to a considerable enhancement of the reaction probability, its combination with vibrational excitation of the broken C-Br bond, (0, 1, 1), results in a strong synergic effect that can be rationalized by the similarity with the classical transitional normal mode. Exciting the C-H stretch has a non-negligible effect on the reaction probability, while for larger translational energies this mode follows the expected spectatorlike behavior. Combination of C-Br stretch and symmetric C-H, (1,0,1), stretch does not show a cooperative effect. Contrary to the spectator mode concept, energy originally stored in the C-H stretching mode is by no means conserved, but almost completely released in other modes of the reaction products. Products are most likely formed in states with a high degree of excitation in the new C-Cl bond, while the internal modes of the methyl group are less important. Reactants with combined umbrella/C-Br stretch excitation, (0, 1, 1), may yield products with two quanta in the umbrella mode.     

248 nm photolysis of CH2Br2 by using cavity ring-down absorption spectroscopy: Br2 molecular elimination at room temperature

Following photodissociation of CH2Br2 at 248 nm, Br2 molecular elimination is detected by using a tunable laser beam, as crossed perpendicular to the photolyzing laser beam in a ring-down cell, probing the Br2 fragment in the B 3Piou+ -X 1Sigmag+ transition. The nascent vibrational population is obtained, yielding a population ratio of Br2(v = 1)Br2(v = 0) to be 0.7 +/- 0.2. The quantum yield for the Br2 elimination reaction is determined to be 0.2 +/- 0.1. Nevertheless, when CH2Br2 is prepared in a supersonic molecular beam under cold temperature, photofragmentation gives no Br2 detectable in a time-of-flight mass spectrometer. With the aid of ab initio potential energy calculations, a plausible pathway is proposed. Upon excitation to the 1B1 or 3B1 state, C-Br bond elongation may change the molecular symmetry of Cs and enhance the resultant 1 1,3A'-X 1A' (or 1 1,3B1-X 1A1 as C2v is used) coupling to facilitate the process of internal conversion, followed by asynchronous concerted photodissociation. Temperature dependence measurements lend support to the proposed pathway.     

Electronic transitions in [Re6S8X6](4-) (X = Cl, Br, I): results from time-dependent density functional theory and solid-state calculations

Relativistic time-dependent density functional theory (TDDFT) calculations were performed on the excited states of the [Re6S8X6](4-) (X = Cl, Br, I) series. For all members of the series, the lowest excited states in the spectra do not correspond to a ligand-to-metal (or ligand-to-cluster) excitation but rather a cluster-cluster transition from the HOMO e(g) to antibonding t(1u) orbitals with only a modest admixture of Re-X sigma* character. These results lead to a re-evaluation of the role of the axial ligand in these compounds. The calculated excitation energies reproduce the experimental absorption and emission spectra. This work also confirms previous TDDFT calculations on the emission energies. Results for discrete cluster ions are compared with those obtained from calculations in the solid state in Cs4[Re6S8X6].CsX (X = Cl, Br) and Cs4[Re6S8I6].2CsI. Significant differences are seen in the relatively higher energies of the antibonding t(1u) orbital in the solid-state case, and an inversion in the orbital character of the two allowed absorptions is calculated. The e(g) (HOMO)-to-a(2g) (LUMO) orbital energy differences corresponding to the emission transition are quite comparable for the solid state and discrete cluster calculations, and both overestimate the observed emission energy by the same margin.