Photophysical properties and vibrational structure of ladder-type penta p-phenylene and carbazole derivatives based on SAC-CI calculations

The ??-conjugated ladder-type molecules constitute an attractive field of organic photoactive materials. In this work, the photophysical properties of ladder-type penta-p-phenylene (LPP) and carbazole derivatives (bisindenocarbazole and diindolocarbazole) have been investigated theoretically using the symmetry-adapted cluster-configuration interaction (SAC-CI) method. The equilibrium geometries in the ground (S ₀) and first excited (S ₁) states were calculated to be planar, and the excitation is delocalized over the molecules. SAC-CI/DZP calculations have been applied to the absorption and emission spectra of these molecules. The absorption spectra were well reproduced in both peak positions and the shape of the absorption bands. The strong absorption is attributed to the highest occupied molecular orbital to the lowest unoccupied molecular orbital (H?CL) transition; however, in carbazoles, the H?C1??L transition is located below the H?CL transition. The vibrational structure in the S ₀?CS ₁ absorption band of LPP was analyzed by calculating the Franck?CCondon (FC) factors based on the potential energy surfaces (PESs) along the normal coordinates that are relevant to the geometry change. The vibrational structure was well reproduced by the theoretical simulation. The C?CC stretching mode dominantly contributes to the vibrational structure, while the breathing motion of the molecular frame does not influence the structure. The emission energies calculated by the SAC-CI method also agree well with the experimental values. The vibrational structure in the fluorescence band was also examined by the FC analysis; the theoretical spectrum is satisfactory for the two carbazoles, while the 0?C0 transition is overestimated in LPP. In diindolocarbazole, the S ₂ state has a large oscillator strength, while the S ₁ state has a small oscillator strength.     

Effect of nuclear spin of a homonuclear molecule on the rate of ion capture

Calculations employing statistical adiabatic channel model show that the spin of a nucleus in a homonuclear molecule affects the rate of ion capture at low temperatures. Whereas for bosons in even electronic states with respect to permutation of the nuclear coordinates (Σ⁺_g,Σ⁻_u) the ion capture rate decreases as the spin increases, for fermions in such states the situation is reversed; the capture rate increases with increasing spin. For the odd Σ⁺_u,Σ⁻_g states the trends are reversed. Such trends are exhibited over the whole region of low temperatures. At very low temperatures the spin effects can become very large. If the effect of the reduced mass contributed by the Langevin rate constant can be ignored, the normal kinetic order at which the isotopomeric molecules capture an ion is reversed. For instance, C₂T₂+H⁺₃ occurs slower than does C₂D₂+H⁺₃.     

A simple determination of the potential energy curves and couplings for long-range charge-transfer reactions. Application to the system (ArN2)+

An original method is presented for calculating long-range energies and couplings of the two (non-adiabatic) states A⁺–B and A–B⁺ of a charge-transfer system (AB)⁺. This method is applied to the calculation of the charge-exchange cross sections in the system (ArN₂)⁺. Concerning the reaction from N₂⁺, we show that the errors made in approximating the interaction energy and the couplings do not affect strongly the values of the cross sections, that most transitions are well described by the Demkov model, and that the evolution of the cross section is governed by the radius R_D (where the coupling is equal to the separation of the states) rather than by the transition probability. We have also obtained qualitative information for the reaction from Ar⁺.     

Molecular states formed by ion beam neutralization of [C2H2]+ and [C2H3]+ on metal targets

A combination of charge-stripping and beam-scattering techniques has been used to study the molecular states formed when a fast beam of [C₂H₂]⁺ and [C₂H₃]⁺ in several isotopic forms are neutralized by electron transfer from metal target atoms (K, Na, Mg and Zn). For [C₂H₃]⁺ the isotopic compositions and relative abundances of product states were found to be insensitive to the method of ion preparation (electron impact and chemical ionization). Ground state neutrals are formed in partial abundance when Mg or Zn is used as a target atom. With low ionization potential targets (K and Na) excitel dissociative states of C₂H₂ and C₂H₃ are formed as major beam constituents. For these states decomposition products have been identified and fragmentation energies measured. The excited states of C₂H₂ and C₂H₃ lie alout 6.8 eV and 2.9 eV, respectively, above their stable ground states. The discussion focuses on the possible identity of the excited states and their structural relations to the precursor ions.     

Analysis and predictions of the vibronic spectrum of the ethynyl radical C2H by ab initio methods

A purely ab initio study of the vibronic structure of the C₂H spectrum in the region up to 7000 cm^?1, which is complicated by the coupling of theX ²Σ⁺ andA ² II systems, is presented. The potential surfaces for the three lowest-lying electronic states 1² A′, 2² A′ and 1² A″ correlating withX ²Σ⁺ andA ² II at the linear molecular geometry are calculated for the various geometrical distortions by means of the multireference configuration interaction (MRD-CI) method. These adiabatic surfaces are transformed into suitable diabatic counterparts. An approach is developed for a simultaneous treatment of three electronic states coupled via the bending and C-C stretching vibrations. Spin-orbit splitting of the vibronic levels and the vibronically averaged values for the hyperfine coupling constants are computed. The results obtained in this study enable a reliable explanation of the available experimental findings of the C₂H spectrum and predict a number of features to be verified by future experiments.     

Excited electronic and ionized states of the nitramide molecule, H2NNO2, studied by the symmetry-adapted-cluster configuration interaction method

Symmetry-adapted-cluster configuration interaction (SAC-CI) wave functions were employed to compute 16 singlet and 13 triplet vertical transitions, and 14 ionized states including relative intensities of the nitramide molecule, H₂NNO₂. This molecule is the simplest neutral closed-shell molecule which has an N–NO₂ bond and is a member of the nitramine family, R,R′N(NO₂), an important class of energetic materials with practical applications. The present nitramide results showed strong similarities with the ones of the N, N-dimethylnitramine molecule, which has also an N–NO₂ bond and was previously studied using the SAC-CI method. Experimental ultraviolet and photoelectron band spectra of the nitramide molecule could be successfully assigned. All the singlet transitions have valence character. The computed singlet and triplet transitions, excepting a singlet one, result from excitation originating in the four highest occupied molecular orbitals, which have close energies. Most of the singlet and triplet transitions involved mixing of singly excited configurations. The strongest computed transition, at 6.8 eV, is a mixture of two nπ_NO2 → π^* configurations corresponding to excitations from the highest occupied molecular orbital (HOMO) to the first two virtual orbitals and has an optical oscillator strength value of 0.2665. The computed ionized states described the whole measured spectrum, have excellent agreement when compared with the measured ionization potentials and revealed an inversion of the ordering of the first states not expected according to Koopmanns’ theorem, thereby showing the limitations of the latter.     

Long-range molecular states dissociating to the three or four lowest asymptotes for the ten heteronuclear diatomic alkali molecules

Long-range energy matrix elements have been calculated in the multipolar expansion approximation for all the molecular states dissociating to the three or four lowest asymptotes for the molecules LiNa, LiK, LiRb, LiCs, NaK, NaRb, NaCs, KRb, KCs and RbCs using the semi-empirical perturbative model we proposed recently. Two different assumptions have been investigated: including or excluding the spin-orbit effects within each atom. Full numerical results are presented for NaK and LiCs which have been chosen as examples. For the ten molecules in the non-interacting assumption the long-range coefficients C₆ and C₈ have been found for each state when neglecting atomic spin-orbit effects while the fitted value C^*₆ and C^*₈ are presented for each state when including atomic spin-orbit effects. When considering the interacting states, those dissociating to ns + n′s and to ns + 5d(Cs) are seen to be slightly perturbed while the states dissociating to ns + n′p and to np + n′s are significantly perturbed. The wavefunctions for the interacting ³Σ⁺, ³Π, 0⁺, 0⁻, 1, 2 states for the molecules NaK and LiCs are presented for various internuclear distances.     

Evidence for long-lived excited states of [CnH2]2+ carbodications

The energetics, structures, stabilities and reactivities of[C_nH₂]²⁺ ions have been investigated using computational methods and experimental mass spectrometric techniques. Spontaneous decompositions of [C_nH₂]²⁺ into [C_nH]⁺ + H⁺ products, observed for ions with odd-n values, have been explained by invoking the formation of excited triplet states. Even-n [C_nH]⁺ ions possess triplet ground states with low-lying excited states, whereas odd-n ions have triplet states with energies several eV above ground singlet states. Radiationless transitions of vibrationally excited long-lived triplet state ions into singlet state continua are suggested as possible mechanisms for spontaneous deprotonation processes of odd-n [C_nH₂]²⁺ ions. Evidence for these long-lived excited states has been obtained in bimolecular single electron transfer reactions.     

Theoretical studies on structures and electronic spectra of linear carbon chains C2nH+ (n = 1−5)

The density functional theory (DFT) and the complete active space self‐consistent‐field (CASSCF) method have been used for full geometry optimization of carbon chains C_2nH⁺ (n = 1–5) in their ground states and selected excited states, respectively. Calculations show that C_2nH⁺ (n = 1–5) have stable linear structures with the ground state of X³Π for C₂H⁺ or X³Σ^? for other species. The excited‐state properties of C_2nH⁺ have been investigated by the multiconfigurational second‐order perturbation theory (CASPT2), and predicted vertical excitation energies show good agreement with the available experimental values. On the basis of our calculations, the unsolved observed bands in previous experiments have been interpreted. CASSCF/CASPT2 calculations also have been used to explore the vertical emission energy of selected low‐lying states in C_2nH⁺ (n = 1–5). Present results indicate that the predicted vertical excitation and emission energies of C_2nH⁺ have similar size dependences, and they gradually decrease as the chain size increases. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

Ab initio excited states calculations of Kr 3 + , probing semi-empirical modelling

The accuracy of the diatomics-in-molecules (DIM) model for the krypton ionic trimer is examined in a series of ab initio calculations. In the C_2v symmetry, the ground states of irreducible representations B₂ and A₁ were calculated using partially spin restricted open-shell coupled cluster method with perturbative triple connections (RHF-RCCSD-T), the relativistic effective core potential (RECP) and an extended basis set of atomic orbitals. Internally contracted multireference configuration interaction method (icMRCI) with the extended and restricted basis set was used to generate the potential energy surfaces (PESs) of the nine electronic states of Kr ₃ ⁺ corresponding to Kr(¹S) + Kr(¹S) + Kr⁺(²P) dissociation limit in a wide interval of nuclear geometries. The overall agreement of the accurate ab initio PESs and the diatomics-in-molecules PESs confirms the quality of the DIM Hamiltonian for the Kr ₃ ⁺ clusters and justifies its use in dynamical and spectroscopic studies of the Kr _n ⁺ clusters. Inclusion of the spin–orbit coupling into the ab initio PESs through a semi-empirical scheme is proposed.     

Lifetimes of C-2 in rotational levels of the B̃2Σ+u state in the gas phase

Lifetimes of C^-₂ in rotational levels of the B?²Σ⁺_u:ν′ = 0, ν′ = 1 states have been measured. C^-₂ was produced from bromoacetylene and rare-gas metastables and the B?²Σ⁺_u—X?²Σ⁺_g transition was laser excited. The lifetimes are constant within a vibrational level, 77 = 8 ns for ν′= 0 and 73 = 7 ns for ν′ = 1. The oscillator strength f_νo = 0.044 ± 0.004.     

Production of C2H4Cl+ by dissociative photoionization of weak molecular complexes in C2H4+HCl mixtures

The photoionization efficiency (PIE) spectrum from 600 to 1200 Å for the production of the ion C₂H₄Cl⁺ by dissociative photoionization of the products of room-temperature jet expansions of a 1:4 mixture of C₂H₄ and HCl was measured at several nozzle pressures. The results were resolved into the PIE yield curve for the heterodimer process C₂H₄·HCl+hv→C₂H₄Cl⁺+H+e. This reaction is necessarily characterized by a large change in geometry between neutral complex and ionic product. The observed spectrum exhibits an unusual and conspicuous peak at 15.2 eV that is characterized by a sharp cutoff to the high energy side. This feature points to the onset of strongly nonstatistical channels for the production of C₂H₄Cl⁺ at this energy such that product formation proceeds through very few states. The observed onset of C₂H₄Cl⁺ at 11.92±0.24 eV is 17±6 kcal mol^?1 above the true threshold. An important conclusion is that at all energies above the onset the yield of dissociative ionization of the heterodimer to the cation C₂H₄Cl⁺ is determined by dynamical factors.     

Time and spectrally resolved fluorescence of Cl*2 and ArCl* in Cl2 doped Ar Under state selective pulsed photoexcitation with synchrotron radiation

Synchrotron Radiation is used to selectively excite chlorine and Cl₂ doped argon in the VUV region. Stationary fluorescence and excitation spectra of the 1¹Σ _u ⁺ , 2¹Σ _u ⁺ and 2³Πg Cl ₂ ^* states and of the ArCl*(B?X) transition are obtained. The excitation threshold of ArCl*(B) in Ar/Cl₂ system is found to be 1,285±5 Å and that of ArCl(C) at ～1,260 Å. The formation of ArCl* and Cl*₂(2³Πg) is discussed in terms of recent potential curves data. A detailed time resolved study is reported which allows us to determine precisely the radiative lifetime of ArCl*(B) state (5.2 ns) and numerous kinetic parameters of this system, to estimate theC state energy and to discuss the relaxation and mixing process of the ArCl*(B) and (C) states. A two ladder multilevel kinetic model is described which accounts for the experimental results and shows the difficulty of studying this particular ArCl* system as compared to the closely related XeCl* and KrCl* ones.     

The first experimental observation of electronic transitions in C2+ and C2D+

High-resolution translational energy spectroscopy (up to 0.1 eV) has been carried out on 8 kV of C₂⁺ and C₂D⁺. The spetra obtained with C₂⁺ formed by different methods show considerable differences which are attributed to the formation of different spin states of the ion. Tentative assignments for the observed transitions have been made including one corresponding to excitation of the ⁴∑_g^? —X ⁴∑_g^? system, which may be useful as a probe of interstellar C₂⁺. Two broad transitions have been seen in the translational energy spectrum of C₂D⁺ which are in reasonable agreement with existing theoretical calculations. Tentative assignments are proposed for these transitions.     

The molecular and electronic structure of radical cations derived from tetramethyltin and hexamethylditin: An SCF-MO study

Molecular geometries and energies have been calculated, using the semi-empirical MNDO method for the closed-shell species SnMe₄, Sn₂Me₆, and (SnMe₃)⁺; and using the UHF-MNDO method for the radicals (SnMe₄)⁺, (Sn₂Me₆)⁺ and SnMe₃^.. The radical cation (SnMe₄)⁺ is calculated to have C_3v skeletal symmetry, with a C_2v isomer some 15 kJ mol^?1 higher in energy. The dinuclear radical cation (Sn₂Me₆)⁺ is calculated to be a σ(SnSn) radical, of D_3d skeletal symmetry: although the calculated Sn(5s) spin density is extremely low, the tin atoms are far from planarity. Calculated spin densities are compared with experimental hyperfine couplings.     

A CAS SCF CI study of the 1Σ+g and 3IIu states of the C2 molecule and the 4Σ−g and 2IIu states of the C+2 ion

Ab initio calculations of the X ¹Σ⁺_g and a ³II_u states of C₂ and the X⁴Σ⁻_g and a²II_u states of the C⁻₂ molecular ion are performed to determine the corresponding potential curves around the potential minima and at the dissociation limits. A large Gaussian basis set augmented by three d-type polarization functions on each carbon center is used to approximate the molecular orbits. The calculations are done at the complete-active-space SCF and multi-reference configuration interactions level. Spectroscopic constants and rotation—vibration energies are derived from the ab initio calculated potentials. Good agreement between theory and experiment is obtained for the X¹Σ⁺_g and a ³II_u states of C₂. In the earlier tentative assignment of the observed electronic transition around 2490 Å to the ²Σ⁻_g ← ²II_u system in C⁺₂, the lower state is confirmed by the present calculations to be C⁺ ₂ (²II_u).     

Jahn—Teller effects in the mindo approximation: structures of the molecular cations of methane and the chloromethanes

The MINDO/3 technique gives geometries for (CH₄)⁺, (CCl₄)⁺ and the intermediate ions (CH_nCl_{4 ? n})⁺ (n = 1, 2, 3) which have symmetries in precise accord with the predictions of the Jahn—Teller effect. The ground state of (CH₄)⁺ has D_2d symmetry, with a C_3v structure ca. 45.6 kJ mol^?1 higher. (CCl₄)⁺ has a C_2v ground state, with a D_2d structure ca. 144 kJ mol^?1 higher: no bound state of C_3v symmetry could be found. (CH₃Cl)⁺ and (CHCl₃)⁺ both have C_s symmetry, and (CH₂Cl₂)⁺ has C_2v symmetry. The analogous fluoro ions are discussed briefly.     

Distinguishing the formation of C2D+4 ions from C2D+6 (by D2 loss) and from C2D5H+ (by HD loss) in a Reflectron spectrometer

The D₂ loss from C₂D⁺₆ ions and the HD loss from C₂D₅H⁺ ions has been investigated in a photoelectron photoion coincidence experiment employing a reflecting ion time of a flight mass spectrometer (Reflectron). The experiment is able to distinguish the metastable formation of C₂D⁺₄ ions (m/z = 32) from C₂D⁺₆ ions by D₂ loss and from C₂D₅H⁺ ions by HD loss simultaneously in a mixture of deuterated ethanes. The breakdown curves of the title reactions are presented and compared to the H₂ loss from C₂H⁺₆ ions. The HD loss from C₂D₅H⁺ is shifted by 67 meV and the D₂ loss from C₂D⁺₆ is shifted by 108 meV with respect to the H₂ loss from C₂H⁺₆. This shift reflects a strong kinetic isotope effect which is most likely due to tunneling of H/D atoms through a barrier.     

The spin-coupling model of zero-field splitting for trimeric [3Fe–4S] and mixed-metal [3FeZn–4S] clusters of ferredoxins from Pyrococcus furiosus

The spin-coupling model of zero-field splitting (ZFS) is developed for trimeric [3Fe–4S] clusters. The correlations between the cluster ZFS parameters D_S and E_S of the states with total spin S and ZFS parameters D_i and E_i of individual ions were obtained for mixed-valent (MV) [3Fe–4S]⁰ clusters with high-spin ground state S_gr=2, for the MV iron core of the hetero-metal [3FeZn–4S]⁺ cluster with S_gr=5/2 and for the monovalent [3Fe–4S]⁺ cluster with S_gr=5/2 of Pyrococcus furiosus ferredoxin (Pf Fd). These correlations and the cluster ZFS parameters D_S and E_S depend on total spin S, intermediate spin S₁₂ and individual spins s_i. The spin-coupling model explains the experimentally observed negative cluster ZFS parameters of MV trimers in the [3Fe–4S]⁰ and [3FeZn–4S]⁺ clusters and the positive cluster ZFS parameter of the tetrameric MV [4Fe–4S]⁺ cluster and the monovalent [3Fe–4S]⁺ trimer of Pf Fd. Single-particle ZFS parameters D_i were obtained for the [3Fe–4S] trimers and [4Fe–4S]⁺ tetramer (S_gr=3/2) of Pf Fd. In distorted trimers, the cluster ZFS parameter D_S of anisotropy changes the value and sign under the variation of isotropic Heisenberg exchange or/and double exchange coupling due to the exchange admixture of the excited states. Experimentally observed peculiarities of effective hyperfine constants A_i for the MV trimer with S_gr=5/2 of the hetero-metal [3FeZn–4S]⁺ cluster were described in the spin-coupling exchange-resonance model with the exchange admixture of the excited states and non-equivalence of the states of different localization.     

Conformational study of the structure of free 12-thiacrown-4 and some of its cation metal complexes

Conformational search of 12-thiacrown-4, 12t4, was performed using the CONFLEX method and the MMFF94S force field whereby 156 conformations were predicted. Optimized geometries of the 156 predicted conformations were calculated at the HF, B3LYP, CAM-B3LYP, M06, M06L, M062x and M06HF levels using the 6-311G** basis set. The correlation energy was recovered at the MP2 level using the same 6-311G** basis set. Optimized geometries at the MP2/6-311G** level and G3MP2 energies were calculated for some of the low energy conformations. The D ₄ conformation was predicted to be the ground state conformation at all levels of theory considered in this work. Comparison between the dihedral angles of the predicted conformations indicated that for the stability of 12t4, a SCCS dihedral angle of 180° requirement is more important than a gauche CSCC dihedral angle requirement. Conformational search was performed also for the 12t4?CAg⁺, Bi³⁺, Cd²⁺, Cu⁺ and Sb³⁺ cation metal complexes using the CONFLEX method and the CAChe-augmented MM3 and MMFF94S force fields. Conformations with relative energies less than 10?kcal/mol at the MP2/6-31+G*//HF/6-31+G* level, with double zeta quality basis set on the metal cations, were considered for computations at the same levels as those used for free 12t4, using also the 6-311G** basis set. The cc-pVTZ-pp basis set was used for the metal cations. The predicted ground state conformations of the 12t4?CAg⁺, Bi³⁺, Cd²⁺, Cu⁺ and Sb³⁺ cation metal complexes are the C ₄, C ₄, C ₄, C _2v and C ₄ conformations, respectively. This is in agreement with the experimental X-ray data for the 12t4?CAg⁺ and Cd²⁺ cation metal complexes, but experimentally by X-ray, the 12t4?CBi³⁺ and Cu⁺ cation metal complexes have C _s and C ₄ structures, respectively.