Theoretical study on S<Subscript>1</Subscript>(<Superscript>1</Superscript>B<Subscript>3u</Subscript>) state electronic structure and absorption spectrum of pyrazine

Making use of a set of quantum chemistry methods, the harmonic potential surfaces of the ground state (S₀(¹ A _g)) and the first (S₁(¹ B _3u)) excited state of pyrazine are investigated, and the electronic structures of the two states are characterized. In the present study, the conventional quantum mechanical method, taking account of the Born-Oppenheimer adiabatic approximation, is adopted to simulate the absorption spectrum of S₁(¹ B _3u) state of pyrazine. The assignment of main vibronic transitions is made for S₁(¹ B _3u) state. It is found that the spectral profile is mainly described by the Franck-Condon progression of totally symmetric mode ν_6a. For the five totally symmetric modes, the present calculations show that the frequency differences between the ground and the S₁(¹ B _3u) state are small. Therefore the displaced harmonic oscillator approximation along with Franck-Condon transition is used to simulate S₁(¹ B _3u) absorption spectra. The distortion effect due to the so-called quadratic coupling is demonstrated to be unimportant for the absorption spectrum, except the coupling mode ν_10a. The calculated S₁(¹ B _3u) absorption spectrum is in reasonable agreement with the experimental spectra. Supported by Taiwan National Science Council (Grant Nos. NSC 96-2113-M-009-021 and NSC 96-2811-M-009-023)     

Theoretical studies on quinones I. The structure of p-benzoquinone and two of its excited triplet states

Ab initio calculations on the ground and two excited triplet states (³B_1g and ³B_1u) of p-benzoquinone are described. The geometries of the three states were fully optimised at the SCF level using the 3-21G basis set. For the excited states, both D_2h and C_2v geometries were investigated. Comparison was made between UHF and ROHF levels of theory.     

Molecular electric properties in electronic excited states: multipole moments and polarizabilities of H2O in the lowest1 B 1 and3 B 1 excited states

Summary The dipole and quadrupole moments and the dipole polarizability tensor components are calculated for the¹ B ₁ and³ B ₁ excited states of the water molecule by using the complete active space (CAS) SCF method and an extended basis set of atomic natural orbitals. The dipole moment in the lowest¹ B ₁ (0.640 a.u.) and³ B ₁ (0.416 a.u.) states is found to be antiparallel to that in the ground electronic state of H₂O. The shape of the quadrupole moment ellipsoid is significantly modified by the electronic excitation to both states investigated in this paper. All components of the excited state dipole polarizability tensor increase by about an order of magnitude compared to their values in the ground electronic state. The present results are used to discuss some aspects of intermolecular interactions involving molecules in their excited electronic states.     

Potential-energy surfaces in the lower excited states of benzene⇌Dewar–benzene isomerization process

Adiabatic potential-energy surfaces in the lower excited states following the benzene?Dewar–benzene isomerization process were calculated by the INDO /S method postulating the concerted reaction mechanism which is proved to be valid in the ground state by the calculation of the intrinsic reaction coordinate. It was concluded that the benzene molecule in the ¹B_1u and ¹E_2u excited states readily isomerizes to Dewar–benzene in the condensed phase although the quantum yield may not be large. Bryce-Smith's proposal, that the isomerization to Dewar–benzene occurs only after the intersystem crossing to the ³B_1u state in benzene molecule, will not be probable; for the ³B_1u route is not favorable to the isomerization in comparison with these singlet routes. However, the rearomatization of Dewar–benzene in the ground state may produce the ³B_1u benzene in small yield with higher yield of the ground-state benzene. The activation energy in the rearomatization is calculated to be 19.03 kcal/mol. These conclusions are consistent with the experimental facts. Molecular orbital correlations in the isomerization and the ionization potentials of Dewar–benzene were also discussed.     

Construction and applications of symmetrized valence bond wave functions

A method constructing symmetry-adapted bonded Young tableau bases is proposed, based on the symmetry properties of bonded tableaus and the projection operator associated with a point group. Several examples including the ground states and π excited states of O₃⁻, O₃, O₃⁺, and C₃⁻ are shown for instruction to construct the symmetrized valence bond (VB) wave function. Excitation energies of transitions from the ground states to π excited states of O₃⁻, C₃H₅, and C₃⁻ are calculated with an optimized symmetrized valence bond wave function in the σ–π separation approximation. Good agreement between the VB and experimental excitation energies is observed. The bonding features of the ground state and the first π excited singlet and triplet states for S₃ are discussed according to bonding populations from VB calculations. Both the singlet-biradical and the dipole structures have significant contributions to the ground state X ¹A₁ of S₃, while the excited state 1 ¹B₂ is essentially composed of the dipole structures, and the 1 ³B₂ excited state is comprised from a triplet-biradical structure. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 66 : 1–7, 1998     

Charge and spin correlation structures of conjugated π systems: Analysis of full CI wave functions of the PPP hamiltonian

An analysis of the electronic correlation structures by means of the charge and spin correlation functions is carried out for full CI wave functions of four, five, and six membered conjugated π systems described by the Pariser–Parr–Pople Hamiltonian. The low-lying states of these systems are classified as covalent (CV ) and ionic (IN ) states depending on whether the probability of finding two electrons simultaneously at the same position is small or large. It is found that many of excited CV states, the typical ones of which are the 2¹A_g state of linear π systems, have stronger CV character than the ground CV state, and their spin coupling structures are different from each other as well as from that of the ground CV state. The spin coupling structure in the ground CV state has an “antiferromagnetic” spin arrangement in favor of antiparallel coupling between nearest neighbor spins while in excited CV states the extent of the antiparallel spin coupling between nearest neighbor sites is decreased. IN states, which are less common for low-lying states than CV ones, are also found to have characteristic modulations in the charge correlation. In particular, the charge correlations in the lowest singlet IN states, 1¹B_u of linear π systems, 1¹B_2g of cyclobutadiene and 1¹B_1U of benzene, are alternating.     

Al,B, and F doped LiNi<Subscript>1/3</Subscript>Co<Subscript>1/3</Subscript>Mn<Subscript>1/3</Subscript>O<Subscript>2</Subscript> as cathode material of lithium-ion batteries

A series of the mixed transition metal compounds, Li[(Ni_1/3Co_1/3Mn_1/3)_1–x-y Al _x B _y ]O_2-z F _z (x = 0, 0.02, y = 0, 0.02, z = 0, 0.02), were synthesized via coprecipitation followed by a high-temperature heat-treatment. XRD patterns revealed that this material has a typical α-NaFeO₂ type layered structure with R3^- m space group. Rietveld refinement explained that cation mixing within the Li(Ni_1/3Co_1/3Mn_1/3)O₂ could be absolutely diminished by Al-doping. Al, B and F doped compounds showed both improved physical and electrochemical properties, high tap-density, and delivered a reversible capacity of 190 mAh/g with excellent capacity retention even when the electrodes were cycled between 3.0 and 4.7 V.     

TiO2基态和激发态的几何结构、激发能和偶极矩

采用二阶微扰理论MP2、密度泛函B3LYP方法和含时密度泛函TD-B3LYP方法分别优化了TiO₂分子的基态¹A₁和六个激发态¹B₂、³B₂、¹B₁、³B₁、¹A₂和³A₂的几何结构. ¹A₁、¹B₂、³B₂、¹B₁和³B₁具有弯曲几何结构, ¹A₂和³A₂具有线性对称结构. 我们发现激发态¹B₂、³B₂、¹B₁和³B₁键偶极矩的数值大小顺序和相应的键角大小顺序完全一致. 另外, 采用完全活化空间自洽场(CASSCF)CASSCF(6,6)、CASSCF(8,8)、多参考组态相互作用(MRCI)和含时密度泛函TD-B3LYP 计算了TiO₂ 分子各激发态的垂直激发能和绝热激发能. 对¹B₂、³B₂和¹B₁三个态, MRCI/CASSCF(6,6) 计算的垂直激发能和绝热激发能与已有的实验值最接近. 对其他三个激发态³B₁、¹A₂和³A₂, 计算的激发能和文献报道的激发能计算值基本一致. 最后, 还计算了TiO₂分子的基态和激发态的偶极矩. 对¹A₁和¹B₂态, 偶极矩的计算值与已有的实验值相吻合. 采用原子偶极矩校正的Hirshfeld 布居方法计算了TiO₂分子在¹A₁、¹B₂、³B₂、¹B₁和³B₁态时各原子的电荷, 发现从基态到激发态偶极矩的变化与电荷从氧原子向钛原子的转移有关. 整个计算中还考察了基函数cc-pVDZ、cc-pVTZ和cc-pVQZ对计算结果的影响.     

Chemical composition optimization and characterization of the NiO/B<Subscript>2</Subscript>O<Subscript>3</Subscript>-Al<Subscript>2</Subscript>O<Subscript>3</Subscript> system as a catalyst for ethylene oligomerization

The samples of the NiO/B₂O₃-Al₂O₃ system with NiO contents from 0.48 to 38.30 wt % were synthesized by the impregnation of borate-containing alumina (20 wt % B₂O₃). It was found that nickel oxide occurred in an X-ray amorphous state in the samples containing to 23.20 wt % NiO. At a NiO content of 4.86 wt % or higher, the support was blocked by the modifier to cause a decrease in the specific surface area from 234 to 176 m²/g and in the amount of acid sites from 409–424 to 333 μmol/g. An extremal character of the dependence of catalyst activity in ethylene oligomerization on NiO content was found with a maximum in the range of 4.86–9.31 wt %. Based on spectroscopic data, it was found that ethylene activation on the NiO/B₂O₃-Al₂O₃ catalyst can be associated with the presence of Ni²⁺ cations, which chemically interact with the support. The catalyst containing 4.86 wt % NiO at 200°C, a pressure of 4 MPa, and an ethylene supply rate of 1.1 h⁻¹ provided almost complete ethylene conversion at the yield of liquid oligomerization products to 90.0 wt %; the total concentration of C⁸⁺ alkenes in these products was 89.0 wt %.     

Potential energy surfaces for OsH2

Summary We compute the potential energy surfaces of 12 electronic states of OsH₂ (four quintet, four triplet, and four singlet) arising from⁵ D ground state of the Os atom as well as triplet and singlet excited states using the complete active space multiconfiguration self-consistent field (CAS-MCSCF) followed by multireference configuration interaction (MRCI) and relativistic CI (RCI) calculation which include up to 430,000 configurations. We find that the⁵ D ground state of Os atom does not insert into H₂ while the excited³ F state of Os does. The³ B ₁ ground state of OsH₂ (there are two other nearly degenerate states) in the absence of spin-orbit coupling was found to be 22 kcal/mol more stable than Os(⁵ D)+H₂. The spin-orbit mixing of³ B ₁,³ B ₂,³ A ₂, and¹ A ₁ states was so strong that it induces significant change in bond angles (up to 10°) for OsH₂.Dedicated to Prof. Klaus RuedenbergCamille and Henry Dreyfus Teacher-Scholar     

Studies on the singlet and triplet states of unsaturated carbenes

Quantum chemical calculations and studies have been made on the different spin states of unsaturated carbenes X₂C?C: and X₂C?C?C: (X?H, Li, F). The geometries and relative stabilities of these carbenes with various groups X have been outlined. The ground states of unsaturated carbenes are all singlet. The energy splittings between the ground states and first excited states ΔE (¹A₁-³B₁) are generally within the value of 60 kcal/mol and change greatly with the electronegativities of groups X, but little with the sizes of the cumulidenes. The equilibrium conformations of ¹A₁ and ³B₁ are different.     

Theoretical study of the electronic spectra ofcis-1,3,5-hexatriene andcis-1,3-butadiene

Summary The electronic spectra forcis-1,3-butadiene andcis-1,3,5-hexatriene have been studied using multiconfiguration second-order perturbation theory (CASPT2) and extended ANO basis sets. The calculations comprise all singlet valence excited states below 8.0 eV, the first 3s, 3p, 3d Rydberg states, and the second 3s state. The four lowest triplet states were also studied. The resulting excitation energies forcis-hexatriene have been used in an assignment of the experimental spectrum, leading to a maximum deviation of 0.13 eV for the vertical transition energies. The calculations place the 1¹ B ₂ state 0.04 eV below the 2¹ A ₁ state. 16 excited states were studied incis-butadiene, using a CASPT2 optimized ground state geometry. The 1¹ B ₂ state was located at 5.58 eV, 0.46 eV below the 2¹ A ₁ state and 0.09 eV above the experimental value. No experimental assignments are available for the 15 other transitions. On leave from: Departmento de Quimica Física, Universidad de Valencia, Dr. Moliner 50, Burjassot, E-46100-Valencia, Spain     

Structure of the 1,3-dinitrobenzene dianion studied by multiconfigurational methods

The structure of the 1,3-dinitrobenzene dianion in the ground and lowest excited electron states was studied by quantum chemical methods. The dianion, unlike the radical anion, is characterized by the symmetrical structure in both the ground triplet (³B₁) and lowest excited singlet (¹A₁) states. The wave function of the singlet state has the biradical character to a great extent. The singlet-triplet splitting calculated by the CASSCF and MRMP2 methods is 6 and 2 kcal mol⁻¹, respectively. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 7, pp. 1408–1410, July, 2007.     

‘Non-Koopmans’ States in Stilbene Cations and a Remarkable Example to the «SDT-Equation»: Indeno [2,1-a]indene

The radical cations of indeno [2, 1-a]indene ( 1 ), stilbene ( 2 ) and 3, 5, 3', 5'-tetramethylstilbene ( 3 ) were prepared by γ-irradiation of the neutral precursors in an electron-scavenging matrix at 77 K . Their electronic spectra were recorded and compared to the photoelectron spectra ( PE .) of the neutral precursors. The results show that either the fourth or the fifth excited doublet state of the cations is of «Non-Koopmans» type, with specific doublet energy (D) D (²B_g)=2.74 eV ( 1 ⁺), =2.59 eV ( 2 ⁺), =2.49 eV ( 3 ⁺). Remarkably, 1 ⁺ possesses two electronic states in the 2.7-2.8 eV energy range: ²A_u («Koopmans»-type) and ²B_g («Non -Koopmans»-type). The «SDT»-equation \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm D} = \sqrt {{\rm S} \cdot {\rm T}} $\end{document} approximately connecting excited singlet (S) and triplet (T) states of a neutral alternant system with the excited doublet (D) states of its radical cation - provided e-promotion occurs For all three excited states between the same (paired) orbitals-is satisfyingly exemplified by 1 : S¹ = 3.92 eV and T¹= 2.06 eV for 1 , D^{4 or 5}=2.74 eV for 1 ⁺.     

Electronic structure and photoelectron spectrum Assignment of allene

In this paper a series of ab initio SCF and configuration calculations were reported forthe ground state and excited states X~2E, A~2E,~2B_2 and ~2A_1 of allene.For ground state X~2E Jahn-Teller distorsion was discussed and a twisted angle of 50° and a torsional barriers of 0.21—0.51 eVwere derived.Based on calculated results,the experimental photoelectron spectrum of allene has beenassigned.     

LCGTO-LSD calculations for CH2

LCGTO-LSD calculations for ground (³B₁) and excited (¹A₁) states of methylene, CH₂, have been performed. Various exchange-correlation potentials and a variety of basis sets (including f functions) have been used. For both states the LSD optimized geometry agrees well with both experimental and the most advanced ab initio results. The correct ground state is found, and the ¹A₁-³B₁ energy separation was found to be ～ 15 kcal/mol, using the “best” local exchange-correlation potential (VWN ), the experimental value being ～ 9 kcal/mol. This result compares favorably with the Hartree-Fock limit separation of 25 kcal/mol. The Kohn-Sham exchange potential leads to a gap of ～26 kcal/mol.     

The relativistic correction to the excitation energy of formaldehyde

First-order perturbation theory for the mass-velocity, Darwin, and magnetic corrections was used with a non-relativistic wavefunction to calculate relativistic contributions to the ground and ³A₂, ³A', ³A₁,²B₂, and ²B₁ excited states of Corrections to the excitation energy were found to be in the range of 30–80 cm^?1.     

Synthesis,Structural Characterization,Photophysics, and Broadband Nonlinear Absorption of a Platinum(II) Complex with the 6‐(7‐Benzothiazol‐2′‐yl‐9,9‐diethyl‐9 H‐fluoren‐2‐yl)‐2,2′‐bipyridinyl Ligand

A platinum complex with the 6‐(7‐benzothiazol‐2′‐yl‐9,9‐diethyl‐9H‐fluoren‐2‐yl)‐2,2′‐bipyridinyl ligand ( 1 ) was synthesized and the crystal structure was determined. UV/Vis absorption, emission, and transient difference absorption of 1 were systematically investigated. DFT calculations were carried out on 1 to characterize the electronic ground state and aid in the understanding of the nature of low‐lying excited electronic states. Complex 1 exhibits intense structured ¹π–π* absorption at λ_abs<440 nm, and a broad, moderate ¹M LCT/¹LLCT transition at 440–520 nm in CH₂Cl₂ solution. A structured ³π–π*/³M LCT emission at about 590 nm was observed at room temperature and at 77 K. Complex 1 exhibits both singlet and triplet excited‐state absorption from 450 nm to 750 nm, which are tentatively attributed to the ¹π–π* and ³π–π* excited states of the 6‐(7‐benzothiazol‐2′‐yl‐9,9‐diethyl‐9H‐fluoren‐2‐yl)‐2,2′‐bipyridine ligand, respectively. Z‐scan experiments were conducted by using ns and ps pulses at 532 nm, and ps pulses at a variety of visible and near‐IR wavelengths. The experimental data were fitted by a five‐level model by using the excited‐state parameters obtained from the photophysical study to deduce the effective singlet and triplet excited‐state absorption cross sections in the visible spectral region and the effective two‐photon absorption cross sections in the near‐IR region. Our results demonstrate that 1 possesses large ratios of excited‐state absorption cross sections relative to that of the ground‐state in the visible spectral region; this results in a remarkable degree of reverse saturable absorption from 1 in CH₂Cl₂ solution illuminated by ns laser pulses at 532 nm. The two‐photon absorption cross sections in the near‐IR region for 1 are among the largest values reported for platinum complexes. Therefore, 1 is an excellent, broadband, nonlinear absorbing material that exhibits strong reverse saturable absorption in the visible spectral region and large two‐photon‐assisted excited‐state absorption in the near‐IR region.     

Theoretical study of the π→π* excited states of linear polyenes: The energy gap between 11Bu+ and 21Ag− states and their character

Multireference perturbation theory with complete active space self-consistent field (CASSCF) reference functions is applied to the study of the valence π→π* excited states of 1,3-butadiene, 1,3,5-hexatriene, 1,3,5,7-octatetraene, and 1,3,5,7,9-decapentaene. Our focus was put on determining the nature of the two lowest-lying singlet excited states, 1¹B_u⁺ and 2¹A_g⁻, and their ordering. The 1¹B_u⁺ state is a singly excited state with an ionic nature originating from the HOMO→LUMO one-electron transition while the covalent 2¹A_g⁻ state is the doubly excited state which comes mainly from the (HOMO)²→(LUMO)² transition. The active-space and basis-set effects are taken into account to estimate the excitation energies of larger polyenes. For butadiene, the 1¹B_u⁺ state is calculated to be slightly lower by 0.1 eV than the doubly excited 2¹A_g⁻ state at the ground-state equilibrium geometry. For hexatriene, our calculations predict the two states to be virtually degenerate. Octatetraene is the first polyene for which we predict that the 2¹A_g⁻ state is the lowest excited singlet state at the ground-state geometry. The present theory also indicates that the 2¹A_g⁻ state lies clearly below the 1¹B_u⁺ state in decapentaene with the energy gap of 0.4 eV. The 0–0 transition and the emission energies are also calculated using the planar C_2h relaxed excited-state geometries. The covalent 2¹A_g⁻ state is much more sensitive to the geometry variation than is the ionic 1¹B_u⁺ state, which places the 2¹A_g⁻ state significantly below the 1¹B_u⁺ state at the relaxed geometry. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 66 : 157–175, 1998