The Low‐Lying Excited States of 2,2′‐Bithiophene: A Theoretical Analysis

The low‐energy regions of the singlet→singlet, singlet→triplet, and triplet→triplet electronic spectra of 2,2′‐bithiophene are studied using multiconfigurational second‐order perturbation theory (CASPT2) and extended atomic natural orbitals (ANO) basis sets. The computed vertical, adiabatic, and emission transition energies are in agreement with the available experimental data. The two lowest singlet excited states, 1¹B_u and 2¹B_u, are computed to be degenerate, a novel feature of the system to be borne in mind during the rationalization of its photophysics. As regards the observed high triplet quantum yield of the molecule, it is concluded that the triplet states 2³A_g and 2³B_u, separated about 0.4 eV from the two lowest singlet excited states, can be populated by intersystem crossing from nonplanar singlet states.     

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.     

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     

Excited states and photochemistry of saturated molecules. extended basics calculations on the 1B1 (1T2) state of methane

The surface of the lowest excited singlet state in methane is analyzed using a basis set composed of 4-31G augmented by a set of one s and three p Rydbergs. The state (1T₂ in T_d symmetry, 1B₁ in C_2v) is found to be dissociative to 1B₁ CH₂ and ground state H₂. Vertically a Rydberg state, 1B₁ rapidly becomes a valence state on distortions from tetrahedral symmetry. Avoided crossings with higher B₁ states are discussed.     

Electric properties of the water molecule in 1A1, 1B1, and 3B1 electronic states: Refined CASSCF and CASPT2 calculations

Summary The dipole moments and dipole polarizabilities of the ¹A₁, ¹B₁, and ³B₁ electronic states of the water molecule have been calculated by using the CASSCF approach followed by the evaluation of the dynamic electron correlation contribution by the second-order perturbation scheme CASPT2. All calculations have been carried out in a specifically extended ANO basis set which accounts for the Rydberg character of the two excited states. In order to estimate the correctness and accuracy of the present data a scan over a variety of different active spaces for the CASSCF wave function has been made. The present results are superior to earlier CASSCF calculations, although their qualitative features remain essentially the same. The dipole moments in ¹B₁ and ³B₁ states are predicted to be about 0.49 a.u. and 0.33 a.u., respectively, and have the opposite orientation with respect to the ground state dipole moment. The dipole polarizability tensors of the excited states are characterized by high anisotropy and are dominated by the in-plane component perpendicular to the symmetry axis. All their components are found to be about an order of magnitude larger than those of the ground state polarizability tensor. The excitation energy dependence on the choice of the active orbital space in the CASSCF reference function is also considered and the analysis of the present data concludes in the concept of what is called the mutually compatible active spaces for the two states involved in excitation. All CASPT2 results are in good agreement with the results of recent calculations carried out in the framework of the open-shell coupled cluster formalism. This agreement confirms the high efficiency of the CASSCF/CASPT2 approach to the treatment of the electron correlation effects.     

The Rydberg Nature And Assignments Of Excited States Of The Water Molecule

We report ab initio theoretical calculation on 32 excited states of H₂ O found to lie below 11.7 eV. Of the eight states observed experimentally, the average discrepancy between theoretical and experimental excitation energies is 0.1 eV. We find that the excited states can each be characterized as arising from an excitation to a Rydberg orbital. Our results indicate that the ? and F? states are both 3d-like excited states rather than one 3d state and one 4s state as previously assumed and similarly for the two Rydberg series joining onto ? and F?. The nsa₁ Rydberg series is found to have a quantum defect of 1.38. joining onto the Ã(¹B₁ state. We have assigned the 9.81 eV transition observed by electron impact as the 1b₁ – 3pb₁ excitation to a ³A₁ state.     

Characterization of the excited states of ethylene by MRCI

The excited states of ethylene are systematically analyzed and characterized according to the natural orbitals (NOs) resulting from multireference configuration interaction singles and doubles (MRCISD) calculations. By comparing the shapes and nodal structures of the NOs with those of hydrogen atomic orbitals, the Rydberg series can be classified. Two or three different types of Rydberg series appear within five excited states for each symmetry of D_2h. For example, in the ¹A_g symmetry there are three series having np and two nf hydrogen‐like atomic orbitals. Electronic correlation effects for the (π→π*) V state are also discussed on the basis of a complete active space self‐consistent field (CASSCF) calculation, showing that electron correlation effects merely within the valence space cannot explain contraction of the V state. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

The electronic states of 1,2,5-oxadiazole studied by VUV absorption spectroscopy and CI, CCSD(T) and DFT methods

The 1,2,5-oxadiazole VUV absorption spectrum in the range 5–11.5 eV, shows broad bands centred near 6.2, 7.1, 8.3, 8.8, 10.6 and 11.3 eV. Rydberg states associated with three ionisation energies (IE) were identified in the complex fine structure above 8.7 eV. Electronic vertical excitation energies for singlet and triplet valence, and Rydberg states were computed using ab initio multi-reference multi-root CI methods. There is generally a good correlation between the envelope of the theoretical intensities and the experimental spectrum. The nature of the more intense calculated Rydberg states, and positions of the main valence and Rydberg bands are discussed. The lowest triplet, singlet and Rydberg 3s excited states have equilibrium structures that are non-planar with C_S symmetry, in a chair-like orientation where the O and H atoms lie out of the NCCN plane. This finding is consistent with the doubling of the low energy UV spectral lines [B.J. Forrest, A.W. Richardson, Can. J. Chem., 50 (1972) 2088].The nearly degenerate IE of the UV-photoelectron spectrum (UV–PES, Palmer et al. 1977) makes analysis of the VUV spectrum difficult, leading to the necessity for reinvestigation. Vertical studies (IE_V) using CI, Tamm–Dancoff (TDA) and Green’s Function (GF) methods all gave similar results, with near degeneracy of the first 3IE_V confirming the earlier study. Studies of the adiabatic IE (IE_A) using CCSD(T) and B3LYP methods, showed the energy sequence ²A₂ < ²B₁ < ²B₂, but these states are all saddle points, in contrast to the 4th state (²A₁) which is a minimum. In contrast, MP2 study of the ²B₂ state showed a minimum, with only two saddle points.Complete minima were found after minor twisting of the structures. The lowest energy cationic state is ²A^″ (C_S), which closely resembles the ²B₂ state. The O–N–C–C skeleton is twisted by 8°. The corresponding ²A^′ state (C_S) is effectively identical to the ²B₁ state. Attempts to find minima for other symmetry states were unsuccessful.     

OClO里德堡态激发能的准确预测及其阴离子低能激发态的从头算研究

采用全活化空间自洽场方法(CASSCF)研究了OClO阴离子7个低能电子态及其自由基的基态. 为了进一步考虑动态电子相关效应, 采用二级多组态微扰理论(CASPT2)获得更加可靠的能量值. 此外, 在ANO-L基组的基础上, 在OClO自由基的电荷中心增加了为研究里德堡态所建立的1s1p1d的波函数, 并应用多组态二级微扰理论(MS-CASPT2)方法获得了里德堡态的准确电子激发能.     

A CASSCF/CASPT2 study on the low‐lying electronic states of the CH3SS and its cation

Complete active space self‐consistent field (CASSCF) and multiconfiguration second‐order perturbation theory (CASPT2) calculations with contracted ANO‐RCC basis set were performed for low‐lying electronic states of CH₃SS and its cation in C_s symmetry. For the ground state X²A″ of CH₃SS, the calculated S‐S stretching mode is in good agreement with experimental reports. The electron transitions of CH₃SS⁺, X¹A′ → 1¹A″, X¹A′ → 2¹A′, and X¹A′ → 2¹A″, are predicted at 1.055, 3.247, and 3.841 eV. Moreover, the calculated adiabatic and vertical ionization potential and adiabatic affinity are in reasonable agreement with the experimental data. The CASSCF/CASPT2 potential energy curves (PECs) were calculated for S₂‐loss dissociation from the X²A″, 1²A′, and 2²A″ states. The electronic states of the CH₃ radical and S₂ molecule as the dissociation products were carefully determined by checking energies and geometries of the asymptote products. The S₂‐loss PEC for CH₃SS indicate that S₂‐loss dissociation occurs from the X²A″ state leading to CH₃ (1²A″) + S₂ (X³Σ), the 1²A′ and 2²A″ leading to CH₃ (1²A″) + S₂ (¹Δ_g). © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012.     

Potential energy curves of several excited states of the Ne2* excimer: Assignment of the transient absorption spectra of the excimer

Most of the excited states of Ne₂, which are correlated with the Rydberg state transitions 2p → 3s, 3p, and 4s of Ne, are studied by ab initio CI calculations. Two transient absorption spectra from the lowest excimer state Σ_u⁺ recently observed by Arai et al., are discussed on the basis of calculated potential energy curves. Possible assignments are presented. The calculated transition energies are in good agreement with the observed ones.     

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     

Ab initio MRD-CI study of the rydberg states of methylene

Potential curves have been calculated for the low-lying Rydberg states of CH₂ as well as for a number of its valence-shell species by employing the ab initio MRD-CI method. The first Rydberg transition is found to occur with a vertical energy of 6.38 eV (1b₁ → 3s), but the corresponding upper state is believed to be strongly predissociated since it correlates directly with the CH(²II) + H(²S_g) ground state fragments at lower energy. The assignment of the first observed Rydberg transition at 8.757 eV by Herzberg as 1b₁ → 3dπ is confirmed almost quantitatively in the calculations, while the corresponding minimum 1P value is computed to be 10.21 eV compared to the experimental result of 10.3 ± 0.1 eV. The dissociation energy of methylene in its ground state is calculated to be 4.47 eV, and this result also fits in well with experimental evidence, which determines a lower limit for this quantity of D₀ > 4.23 eV. Finally, it is found that none of the Rydberg states nor any of the higher-lying valence-shell species of methylene are of sufficiently low energy to play a significant role in the experimental determination of the ¹A₁-³B₁ splitting of this system.     

Conical Intersections and Low‐Lying Electronic States of Tetrafluoroethylene

The low‐lying electronic states of tetrafluoroethylene (C₂F₄) are characterized theoretically for the first time using equation‐of‐motion coupled cluster theory (EOM‐CCSD), and complete active space self‐consistent field (CASSCF) and second‐order perturbation theory (CASPT2). Computations are performed for vertical excitation energies, equilibrium geometries, minimum‐energy conical intersections, and potential energy curves along three geometric coordinates: 1) twisting of the F?C?C?F dihedral angle, 2) pyramidalization of the CF₂ group, and 3) migration of a fluorine atom resulting in an ethylidene‐like (CF₃CF) structure. The results suggest two relaxation pathways from the Rydberg‐3s excited electronic state to the ground state. These relaxation pathways are discussed in conjunction with the femtosecond photoionization spectroscopy results of Trushin et al. [ChemPhysChem­ 2004 , 5, 1389].     

Photodeactivation paths in norbornadiene

The first high level ab initio quantum‐chemical calculations of potential energy surfaces (PESs) for low‐lying singlet excited states of norbornadiene in the gas phase are presented. The optimization of the stationary points (minima and conical intersections) and the recalculation of the energies were performed using the multireference configuration interaction with singles (MR‐CIS) and the multiconfigurational second‐order perturbation (CASPT2) methods, respectively. It was shown that the crossing between valence V₂ and Rydberg R₁ states close to the Franck–Condon (FC) point permits an easy population switch between these states. Also, a new deactivation path in which the doubly excited state with (π₃)² configuration (DE) has a prominent role in photodeactivation from the R₁ state due to the R₁/DE and the DE/V₁ conical intersections very close to the R₁ and DE minima, respectively, was proposed. Subsequent deactivation from the V₁ to the ground state goes through an Olivucci–Robb‐type conical intersection that adopts a rhombic distorted geometry. The deactivation path has negligible barriers, thereby making ultrafast radiationless decay to the ground state possible. © 2013 Wiley Periodicals, Inc.     

Theoretical prediction on HAlS+ and HSAl+ cations using multiconfiguration second‐order perturbation theory

Some low‐lying states of the HAlS⁺ and HSAl⁺ cations have been studied for the first time by large‐scale theoretical calculations using three methods: complete active space self‐consistent field (CASSCF), complete active second‐order perturbation theory (CASPT2), and density functional theory Becke's three‐parameter hybrid function with the nonlocal correlation of Lee–Yang–Parr (B3LYP) with the contracted atomic natural orbital (ANO‐L) and cc‐pVTZ basis sets. The geometries of all stationary points along the potential energy surfaces (PESs) were optimized at the CASSCF/ANO‐L and B3LYP/cc‐pVTZ levels. The ground and the first excited states of linear HAlS⁺ are predicted to be X²Π and A²Σ⁺ states, respectively. For the linear HSAl⁺ structure, the first excited state is A²Σ⁺. The X²Π state of linear HSAl⁺ is a second‐order saddle point, because it has two imaginary frequencies. Two bent global minima M1 and M2 were found along the 1²A′ and 1²A″ PESs, respectively. The CASPT2/ANO‐L potential energy curves of isomerization reactions were calculated as a function of HAlS bond angle. According to our calculations, the ground‐state HAlS⁺ is linear, whereas the ground‐state HSAl⁺ is bent. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Exploring concerted effects of base pairing and stacking on the excited‐state nature of DNA oligonucleotides by DFT and TD‐DFT studies

We have taken (dA)₅, (dT)₅, and (dA)₅·(dT)₅ as model systems to study concerted effects of base pairing and stacking on excited‐state nature of DNA oligonucleotides using density functional theory (DFT) and time dependent DFT methods. The spectroscopic states are determined to be of a partial A → A charge‐transfer nature in the A·T oligonucleotides. The T → T charge‐transfer transitions produce dark states, which are hidden in the energy region of the steady‐state absorption spectra. This is different from the previous assignment that the T → T charge‐transfer transition is responsible for a shoulder at the red side of the first strong absorption band. The A → T charge‐transfer states were predicted to have relatively high energies in the A·T oligonucleotides. The present calculations predict that the T → A charge‐transfer states are not involved in the spectra and excited‐state dynamics of the A·T oligonucleotides. In addition, the influence of base pairing and stacking on the nature of the ¹nπ* and ¹ππ* states are discussed in detail. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

All-valence-electron CI treatment of the electronic spectrum of trans-butadiene

An all-valence-electron CI treatment is reported for the low-lying valence and Rydberg states of butadiene. All singly- and doubly-excited configurations relative to a series of the leading terms in a given CI expansion are taken into account, with resulting secular equation orders of as high as 150 000. The agreement between calculated and experimental transition energies is invariably better than 0.2 eV where comparison is possible, with all low-lying valence triplet and Rydberg singlet excited states being unambiguously assigned. The valence-shell excitation to the 2 ¹A_g species is concluded to correspond to the 7.06 eV band system, while the forbidden singlet—singlet transition reported by McDiarmid is assigned as x₂ → 3s. The possibility of an avoided crossing between Rydberg valence ¹B_u excited states having a determining influence on the appearance of the broad intense V₁—N absorption is also discussed.     

Photoisomerization Mechanism of Ruthenium Sulfoxide Complexes: Role of the Metal‐Centered Excited State in the Bond Rupture and Bond Construction Processes

Phototriggered intramolecular isomerization in a series of ruthenium sulfoxide complexes, [Ru(L)(tpy)(DMSO)]ⁿ⁺ (where tpy=2,2’:6’,2’’‐terpyridine; DMSO=dimethyl sulfoxide; L=2,2’‐bipyridine (bpy), n=2; N,N,N’,N’‐tetramethylethylenediamine (tmen) n=2; picolinate (pic), n=1; acetylacetonate (acac), n=1; oxalate (ox), n=0; malonate (mal), n=0), was investigated theoretically. It is observed that the metal‐centered ligand field (³MC) state plays an important role in the excited state S→O isomerization of the coordinated DMSO ligand. If the population of ³MC_S state is thermally accessible and no ³MC_O can be populated from this state, photoisomerization will be turned off because the ³MC_S excited state is expected to lead to fast radiationless decay back to the original ¹GS_S ground state or photodecomposition along the Ru²⁺?S stretching coordinate. On the contrary, if the population of ³MC_S (or ³MC_O) state is inaccessible, photoinduced S→O isomerization can proceed adiabatically on the potential energy surface of the metal‐to‐ligand charge transfer excited states (³MLCT_S→³MLCT_O). It is hoped that these results can provide valuable information for the excited state isomerization in photochromic d⁶ transition‐metal complexes, which is both experimentally and intellectually challenging as a field of study.     

Theoretical study on the vertical electronic spectrum of carbonyl fluoride,F2CO

Ab initio self-consistent-field (SCF ) and configuration interaction (CI ) calculations on the ground and excited states of carbonyl fluoride (F₂CO) were carried out at its experimental ground-state equilibrium geometry. Vertical transition energies deduced from the CI results provide assignments for the electronic systems I–IV, experimentally observed by Workman and Duncan. The singlet excited state, ¹A₁ (π→π*), is found to be a mixed valence–Rydberg state and to he 1 to 1.2 eV above the suggested experimental value, irrespective of the choice of the basis used for the CI calculations.