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.     

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     

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.     

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)     

The Role of the nπ* 1Au State in the Photoabsorption and Relaxation of Pyrazine

The geometric, energetic, and spectroscopic properties of the ground state and the lowest four singlet excited states of pyrazine have been studied by using DFT/TD‐DFT, CASSCF, CASPT2, and related quantum chemical calculations. The second singlet nπ* state, ¹A_u, which is conventionally regarded dark due to the dipole‐forbidden ¹A_u←¹A_g transition, has been investigated in detail. Our new simulation has shown that the state could be visible in the absorption spectrum by intensity borrowing from neighboring nπ* ¹B_3u and ππ* ¹B_2u states through vibronic coupling. The scans on potential‐energy surfaces further indicated that the ¹A_u state intersects with the ¹B_2u states near the equilibrium of the latter, thus implying its participation in the ultrafast relaxation process.     

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.     

Non-radiative decay of the benzene 1B2u and 3B1u states

Optic-acoustic measurements on high pressure benzene are presented, and are used to analyse the nature of the decay channels form the highly vibrationally excited ³B_1u state. The vibrationally relaxed benzene ³B_1u state is deactivated by n-pentane with a collisional efficiency of 3 × 10^?5. A model, introducing an intermediate state close in energy to the ³B_1u state, is shown to be in good accord with the results.     

Absorption,resonance, and near‐resonance Raman studies of the tetracyanoquinodimethane neutral and its monoanion in terms of density functional theory and complete active space self‐consistent field methods

The electronic structure of the 1¹B_1u and 1²B_3u excited electronic states of the tetracyanoquinodimethane (TCNQ) neutral and its charged derivative are studied within the framework of complete active space self‐consistent field (CASSCF) and Becke's three‐parameter hybrid method with Lee–Yang–Parr correlation functional (B3LYP) methods applied to the level aug‐cc‐p‐VDZ basis set. Both CASSCF/aug‐cc‐p‐VDZ and B3LYP/aug‐cc‐p‐VDZ treatments provide the ground‐state and the excited state geometries; these are then used to assess the Franck–Condon (FC) parameters in the 1¹B_1u state of the neutral TCNQ and in the 1²B_3u state of the TCNQ monoanion. The quality of numerical results is then tested on the base of available experimental near‐resonance and resonance Raman data. The studies are performed in terms of the vibronic model, which takes both FC and mode‐mixing (Dushinsky) effects into account. This somewhat simplified vibronic model leads to very good agreement between the theory and the Raman experiments concerning both neutral TCNQ and its monoanion. In particular, the calculated excitation profiles of the ν₂ = 2215 cm^?1, ν₄ = 1389 cm^?1, ν₅ = 1195 cm^?1, and ν₉ = 336 cm^?1 fundamentals are shown to be in excellent agreement with those for the TCNQ monoanion. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

1 Bu–2 Ag conical intersection in trans-butadiene: ultrafast dynamics and optical spectra

The potential-energy functions of the 1 ¹B_u and 2 ¹A_g excited valence states of trans-butadiene have been characterised by the CASPT2 method. Based on these ab initio data, a vibronic-coupling model describing the conical intersection of the 1 ¹B_u and 2 ¹A_g states has been constructed. UV resonance-Raman and absorption spectra have been calculated, employing the time-dependent approach. The time-dependent wave-packet calculations reproduce the expected ultrafast (≈30 fs) radiationless decay of the optically bright 1 ¹B_u state into the dark 2 ¹A_g state.     

Absorption spectrum of manganian andalusite: Cluster calculation by an ab initio method

The ground state and the first few excited states of an MnO₆^9? cluster are calculated in the unrestricted Hartree–Fock model. The state ordering is ⁵B_{1 g}, ⁵A_{1 g}, ⁵B_{2 g}, and ⁵E_g as can be expected from simpler models. Consistent with the results by the same method for copper complexes, we obtain d–d transition energies about one half or less of the experimental energies. The charge transfer spectrum is subject to a large spin polarization in the sense that the lowest charge transfer state (⁵E_u) has five unpaired spins on Mn.     

Two-photon absorption in the collisionless gas phase: lifetimes of new vibrational levels in benzene

Two-photon photoselection has been demonstrated for a molecule in the low pressure gas phase. The excitation has been used to populate new vibrational levels in benzene under isolated molecule conditions down to 0.1 torr. The new states display unusual behaviour as compared to the lifetimes of one-photon excited states. Most unexpectedly the lifetimes of the strongest two-photon inducing mode ν₁₄ is longer than all other lifetimes, including that of the vibrationless ¹B_2u origin. Some theoretical explanations are offered.     

Small nickel clusters: Two low-lying Ni<Subscript>3</Subscript> states

Matrix isolation IR spectroscopy and quantum-chemical calculations were jointly used to identify the system of bands related to Ni₃ clusters. The positions of two low-lying electronic states were determined, and vibrational frequencies and geometry in the ground and excited states were estimated. In all the calculated states, Ni₃ had the structure of an isosceles triangle. In the X ³ B ₂ ground and a ³ B ₁ lower excited states, this was an acute-angled triangle. In the b ³ B ₂ and c ³ B ₁ excited states, the triangle was obtuse-angled.     

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.     

Exponentially generated wave functions and excited states of benzene

Usefulness of the exponentially generated wave function approach is shown. We first give an overview of the SAC (symmetry adapted cluster) and SAC-CI study on the valence and Rydberg excitations and ionizations of benzene including both and spaces. The importance of the reorganization effect is found for the T₃(³B_2u), S₂(¹B_1u), and S₃(¹E_1u) states, so-called V states. A first systematic calculation is reported for the Rydberg excited states. Next, the idea of the exponentially generated wave function (EGWF) theory is explained. New exponential-type operators and new wave functions associated with them are defined. The mixed or multi use of these exponential operators is shown to be effective both physically and practically. We call the resultant wave functions MEG (multi-exponentially generated) wave functions. We then explain the algorithm of calculations and show some results on the potential energy curves of the ground, excited, and quasi-degenerate states of some diatomics and triatomics.     

A CASSCF study on the lowest π→π* excitation of urocanic acid

The photochemical cis/trans isomerization of urocanic acid (UCA, (E)‐3‐(1′H‐imidazol‐4′‐yl)propenoic acid) was investigated using complete active space SCF (CASSCF) ab initio calculations. The singlet ground state and the triplet and the singlet manifolds of the lowest‐lying π→π* (HOMO→LUMO) excitation of the neutral and the anionic UCA were calculated using the 6‐31G* and the 6‐31+G* basis sets, respectively. The torsional barrier of the double bond of the propenoic acid moiety in UCA is observed to be considerably lower in the T₁ and S₁ excited states of the neutral UCA and in the T₁ but not in the S₁ excited state of the anionic UCA, as compared to the S₀ state of the respective protonation form. The cis‐isomer of both the neutral and the anionic UCA is lower in energy than the trans‐isomer in the S₀, T₁, and S₁ states. This energy difference is larger in the excited states than in the ground state, probably due to strengthening of the intramolecular hydrogen bond of cis‐UCA as the molecule is excited. The results of the calculations, interpreted in terms of the idea that UCA is deprotonated upon electronic excitation, led to construction of a new model for the photoisomerization mechanisms of UCA. According to this model, the trans‐to‐cis isomerization proceeds via both the triplet and the singlet manifolds in the deprotonated form of UCA. This isomerization may occur in the S₀ state of the neutral UCA as well. The cis‐to‐trans isomerization is suggested to proceed only in the S₀ state of the neutral UCA. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 72: 25–37, 1999     

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     

Absolute fluorescence quantum yields for vapour-phase benzene and naphthalene,and comments on the non-radiative processes

Optic—acoustic measurements have been employed in the determination of absolute quantum yields for benzene and naphthalene. Heat yields are measured by a method using oxygen quenching of both triplet and singlet states. For vibrationally relaxed excited singlet states the fluorescence quantum yields, φ^B_f, are 0.16 ± 0.02 and 0.79 ± 0.02 for benzene and naphthalene respectively. For 0.07 torr naphthalene at room temperature with 248 nm excitation, φ_f = 0.35 ± 0.03 and the quantum yield of internal conversion is less than 0.05. The decay of the highly vibrationally excited triplet state is dominated by vibrational relaxation for 0.07 torr naphthalene, but for benzene, even at high pressures, strong competition comes from an indirect coupling process to the ground state.     

Molecular spectroscopy of 2,5-distyrylpyrazine

The molecular absorption and fluorescence spectra of 2,5-distyrylpyrazine (DSP) in a Shpol'skii matrix at 4 K together with the Raman spectrum of crystalline samples at 298 K have been investigated. The transition to the lowest excited singlet state of B_u symmetry is of π—π^* character and two sites with origins at 23621 cm^?1 and 23713 cm^?1 are observed in n-tetradecane at 4 K. The DSP molecule has the same conformation in the two sites and, furthermore, the geometry of the molecule in the first excited singlet states is unchanged as compared to the ground state. The vibrational progression observed for DSP is compared with the literature data for distyrylbenzene (DSB) and slilbene.     

Density of states due to donor-pair molecules in three- and two-dimensional semiconductor systems

The density of states is calculated for a random distribution of donor-pairs of hydrogenlike impurities in three- and two-dimensional systems. Recent investigations of the hydrogen molecule in the alternant–molecular–orbital approximation are here extended. We found that the lowest excited state ¹Σu (i.e., H⁺H^?), which is optically connected to the ground state, plays a relevant role in the absorption spectra of semiconductor systems.