Physical origins of high-order Born-Oppenheimer electronic polarizabilities: Application to a 30th-order perturbation study of H2+

A method is developed for investigating the physical origins of high-order Born-Oppenheimer (BO) electronic polarizabilities for diatomic molecules; the procedure is based upon resolution of the polarizabilities in each order into their kinetic, internal-potential, and field-potential energetic components. The energetic components of BO polarizabilities are subject to a priori constraints on their relative magnitudes and signs which are similar to but less restrictive than.those for non-Born-Oppenheimer (NBO) polarizabilities. The procedure, implemented via the perturbational-variational Rayleigh-Ritz formalism, is illustrated by a 30th-order polarizability study of the ground state of BO H₂⁺. The BO results are compared to those for NBO H₂⁺ and their differing behaviour is discussed. Other diatomic molecules are considered.     

RESONANCE RAMAN SPECTRUM OF THE EXCITED 21Ag STATE OF ß-CAROTENE

Abstract— Resonance Raman (RR) bands assignable to the 2¹A_g excited state of ß-carotene are recorded using picosecond time-resolved resonance Raman (PTR³) spectroscopy. The RR spectrum contains bands in both the C-C (1204 cm^?1, 1243 cm^?1, and 1282 cm^?1) and C=C (1777 cm^?1) stretching regions. The time-dependent intensities of these RR features, measured with ? 30 ps. resolution, are found (i) to closely correlate with picosecond transient absorption (PTA) data recorded at 575 nm on the same sample and (ii) inversely correlate with the time-dependent intensities of RR bands assigned to the 1¹A_g ground state. Both of these observations support the assignment of these four RR features to the 2¹A_g excited state. These results remove uncertainties associated with earlier experiments in which excited-state RR scattering from (3-carotene was not observed in spite of predicted trends emanating from studies of shorter polyene compounds. The observed C=C band position also agrees with a recent report of this feature.     

Geometries, electronic structures, and excited states of UN2, NUO+, and UO 2 2+ : a combined CCSD(T), RAS/CASPT2 and TDDFT study

The ground- and excited-state geometries and electronic structures of the isoelectronic series of molecules UN₂, NUO⁺, and UO ₂ ²⁺ are investigated by using relativistic density functional theory (DFT) and ab initio wavefunction theory (WFT). Scalar relativistic and spin?Corbit-coupled quantum chemical methods at the CASPT2, RASPT2, CCSD(T), DFT and TDDFT levels are applied. Relativistic effects as elucidated by Pekka Pyykk? play an important role in these uranium compounds, in particular for the excited states. The three molecular species exhibit significantly different spectroscopic properties, concerning their excitation energies, bond lengths and vibrations. Density functional approaches yield qualitatively correct results for the ground states and the valence????U.7s,6d excited states. However, the performance of TDDFT for valence????U.5f type excitations (in particular of UN₂ and NUO⁺) is less satisfactory, indicating the importance of the self-interaction correction for such excitations.     

Acid-Base Properties of the Ground and Excited States of Ruthenium(II) Tris(4′-methyl-2,2′-bipyridine-4-carboxylic Acid)

The acid dissociation constant, pK_a, for the ground and excited states of ruthenium tris(4′-methyl-2,2′-bipyridine-4-carboxylic acid) complex have been measured. The ground state pK_a obtained from the pH titration curve of the complex absorption at 454 nm was 2.5. The lifetimes of the excited-state for deprotonated and protonated ruthenium complexes are 595 and 150 ns, respectively. The excited-state pK_a* is obtained from the emission titration curve at 630 nm and corrected for the excited-state lifetime to be 4.2. The increase of 1.7 pH units in the acid dissociation constant in the excited-state indicates that the ligand is much more basic in the excited-state. This result confirms the MLCT assignment for the lowest electronic transition of [Ru(mbpyCOOH)₃]²⁺.     

An ab initio study of electronic spectra and excited-state properties of 7-azaindole in vapour phase and aqueous solution

The geometries of 7-azaindole (7AI), its tautomer (7AT), and 7AI–H₂O and 7AT–H₂O complexes were optimised in the ground state and some low-lying singlet excited states using the 3-21G basis set. Differences of total energies of the optimised ground and excited states and the vertical excitation energies of these systems were used to explain the observed electronic spectra. Effect of solvation of these systems in bulk water was studied using the polarized continuum model (PCM). The mode of binding of a water molecule in the S₂(n–π^*) excited state of 7AI was found to be quite different from those in its ground and π–π^* excited states. It is shown that crossing of the lowest two singlet excited-state potential surfaces S₁(π–π^*) and S₂(n–π^*) of 7AI occurs in the vapour phase under geometry relaxation while on interaction with water, the S₂(n–π^*) excited state is raised up appreciably going even above the S₃(π–π^*) excited state. Ground- and excited-state molecular electrostatic potential mapping was carried out, which led to valuable information regarding the nature of excited states of the above-mentioned systems.     

Fast calculation of excited-state potentials for rare-gas diatomic molecules: Ne2 and Ar2

A fast method for obtaining excited-state potentials of rare-gas diatomic molecules is described. Two types of excited orbitals are used: molecular orbitals calculated in the field of a singly charged molecular ion, and atomic orbitals (properly symmetrized) obtained in a similar atomic system. The RPA equations are solved within the manifold of excitations from the highest occupied orbital in each symmetry to the lowest excited orbital of either type in each symmetry. A simple model for estimating the dynamic correlation correction to excitation (and ionization) energies is given. Applications to excited states of Ne₂(^1,3Σ⁺_{g, u}, ^1,3Π_{g, u}) and Ar₂(^1,3Σ⁺_{g, u}) are described. Two-electron integral transformations involve only three orbitals of each symmetry, and the RPA matrices are four-dimensional. The computational effort required for all excited-state potentials adds less than one-tenths (in terms of computer time) to the effort involved in the preliminary ground state Hartree—Fock calculations. The resulting potentials compare favorably with more elaborate CI calculations and give good agreement with spectroscopic and scattering data. Potential curves for the molecular ions are also given.     

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.     

Singlet and Triplet Excited States and Intersystem Crossing in Free‐Base Porphyrin: TDDFT and DFT/MRCI Study

Extensive time-dependent DFT (TDDFT) and DFT/multireference configuration interaction (MRCI) calculations are performed on the singlet and triplet excited states of free-base porphyrin, with emphasis on intersystem crossing processes. The equilibrium geometries, as well as the vertical and adiabatic excitation energies of the lowest singlet and triplet excited states are determined. Single and double proton-transfer reactions in the first excited singlet state are explored. Harmonic vibrational frequencies are calculated at the equilibrium geometries of the ground state and of the lowest singlet and triplet excited states. Furthermore, spin–orbit coupling matrix elements of the lowest singlet and triplet states and their numerical derivatives with respect to nuclear displacements are computed. It is shown that opening of an unprotonated pyrrole ring as well as excited-state single and double proton transfer inside the porphyrin cavity lead to crossings of the potential energy curves of the lowest singlet and triplet excited states. It is also found that displacements along out-of-plane normal modes of the first excited singlet state cause a significant increase of the 2|H_so|S₁>, 1|H_so|S₁>, and 1|H_so|S₀> spin–orbit coupling matrix elements. These phenomena lead to efficient radiationless deactivation of the lowest excited states of free-base porphyrin via intercombination conversion. In particular, the S₁→T₁ population transfer is found to proceed at a rate of ≈10⁷ s⁻¹ in the isolated molecule.     

The energy balance and branching ratios associated with the chemiluminescent reaction Si(3P) + N2O(1Σ) → SiO*(a3Σ+, b3Π, A1Π) + N2(υ″ ⩾ 5) — possible formation of vibrationally excited N2

Silicon atoms react under single collision conditions with N₂O to yield chemiluminescent emission corresponding to the SiO a³Σ⁺?X¹Σ⁺ and b³Π?X¹Σ⁺ intercombination systems and the A¹Π?X¹Σ⁺ band system. A most striking feature of the SiN₂O reaction is the energy balance associated with the formation of SiO product molecules in the A¹Π and b³Π states. A significant energy discrepancy ( = 10000 cm^? = 1.24 eV) is found between the available energy to populate the highest energetically accessible excited-state quantum levels and the highest quantum level from which emission is observed. It is suggested that this discrepancy may result from the formation of vibrationally excited N₂ in a concerted fast SiN₂O reactive encounter. Emission from the SiO a³Σ⁺ (A¹Π) and b³Π(A¹Π, E¹Σ₀⁺) triplet-state manifold results primarily from intensity borrowing involving the indicated singlet states. Perturbation calculations indicate the magnitude of the mixing between the b³Π, A¹Π and E¹Σ₀⁺ states ranges between 0.5 and 2%. On the basis of these calculations, the branching ratio (excited triplet)/(excited singlet) is found to be well in excess of 500. An approximate vibrational population distribution is deduced for those molecules formed in the b³Π state. The present studies are correlated with those of previous workers in order to provide an explanation for diverse relaxation effects as well as observed changes in the ratio of a³Σ⁺ to b³Π emission as a function of pressure and experimental environment. Some of these effects are attributable to a strong coupling between the a³Σ⁺ and b³Π state. Based on the current results, there appears to be little correlation between either (1) the branching ratio for excited state formation or (2) the total absolute cross section for excited-state formation and (3) the measured quantum yield for the SiN₂O reaction. Implications for chemical laser development are considered.     

A comparison of ground- and excited-state properties of [Ru(bz)2]2+ and bis(η6-benzene)ruthenium(II) p-toluenesulfonate using the density functional theory

The ground- and excited-state properties of both [Ru(bz)₂]²⁺ and crystalline bis(η⁶-benzene)ruthenium(II) p-toluenesulfonate are investigated using the density functional theory. A symmetry-based technique is employed to calculate the energies of the multiplet structure splitting of the singly excited triplet states. For the crystalline system, a Buckingham potential is introduced to describe the intermolecular interactions between the [Ru(bz)₂]²⁺ system and its first shell of neighbor molecules. The overall agreement between experimental and calculated ground- and excited-state properties is good, as far as the absolute transition energies, the Stokes shift, and the geometry of the excited states are concerned. The calculated d-d excitation energies of the isolated cluster are typically 1000–2000 cm⁻¹ too low. An energy lowering is obtained in a_1g→e_1g(³E_1g) excited state when the geometry of [Ru(bz)₂]²⁺ is bent along the e_1u Renner–Teller active coordinate. It vanishes as the crystal packing is taken into account. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1343–1353, 1999     

Raman spectroscopy from a picosecond-lived excited state of methyl orange

Vibrational Raman scattering from a picosecond-lived excited state of methyl orange in 9 N H₂SO₄ is reported. The vibrational frequencies of normal modes in ground and electronic excited states are separated by ≈ 10 cm^?1 but rather large differences exist in their intensities. In particular, the intensity of a mode at ≈ 1180 cm^?1, due to the NN stretch, is sensitive to the frequency of the nanosecond pulsed tunable laser. A bandwidth comparison between ground- and excited-state spectra reveals that the widths of bands of the latter, like that of the former are due to dephasing and other effects associated with interaction of molecules in the liquid phase.     

Nonradiative Excited-State Decay via Conical Intersection in Graphene Nanostructures

Chemical groups are known to tune the luminescent efficiencies of graphene-related nanomaterials, but some species, including the epoxide group (−COC−), are suspected to act as emission-quenching sites. Herein, by performing nonadiabatic excited-state dynamics simulations, we reveal a fast (within 300 fs) nonradiative excited-state decay of a graphene epoxide nanostructure from the lowest excited singlet (S₁) state to the ground (S₀) state via a conical intersection (CI), at which the energy difference between the S₁ and S₀ states is approximately zero. This CI is induced after breaking one C−O bond at the −COC− moiety during excited-state structural relaxation. This study ascertains the role of epoxide groups in inducing the nonradiative recombination of the excited electron-hole, providing important insights into the CI-promoted nonradiative de-excitations and the luminescence tuning of relevant materials. In addition, it shows the feasibility of utilizing nonadiabatic excited-state dynamics simulations to investigate the photophysical processes of the excited states of graphene nanomaterials.     

The calculation of ground and excited doublet state molecular polarizabilities by the CNDO/S-CI method

The calculation of ground and excited state molecular polarizabilities by the CNDO/S-CI method has been extended to include doublet states. As incorporated, the second order perturbation scheme usually predicts average state polarizabilities of molecular cation ground states to be lower than the corresponding singlet ground states. Average anion polarizabilities are generally found to be higher than those of the corresponding singlet states. Excited doublet state polarizabilities are presented for the molecular cation of formaldehyde, benzene, 1,3,5-trans-hexatriene, and naphthalene. Due to the unavailability of experimental data it is currently impossible to assess appropriately the quality of these results.     

Picosecond photophysics of diphenylpolyenes: evidence for the influence of excited-state conformational changes on the energy gap ΔE(Bu*-Ag*)

B_u and A_g excited singlet states are directly observed in DPH (all-trans-1,6-diphenylhexatriene) and DPO (all-trans-1,8-diphenyloctatetraene) using picosecond transient absorption spectroscopy. Two absorption bands near 4800 and 6500 Å are observed and assigned to B_u and A_g excited singlet states, respectively. Time-resolved evolution, on a picosecond time scale, shows that in both DPO and DPH a thermal equilibrium exists between the B_u and A_g states with a non-negligible B_u population at room temperature even in DPO. Temperature variations enable us to deduce the energy gap ΔE between these two states. It is shown that conformational changes, including the solvent cage effect, significantly influence the ΔE value which is less in the excited-state than in the ground-state conformation.     

Density functional calculations of optical excitation energies by a transition-state method

Optical excitation energies of MnO⁻₄, CrO²⁻₄, and RuO₄ are calculated using the density functional methodology. A short outline of some important developments in this theory for the determination of excited-state properties is given. A practical working procedure for the calculation of transition energies including multiplet splitting is described. This method is based on a transition-state approach which is connected, as will be shown, to Slater's transition-state concept. Results obtained by this working procedure are compared to the energy differences between separately converged configurations of ground and excited states and the corresponding multiplet structure, denoted as the ΔSCF calculation in the following. © 1997 John Wiley & Sons, Inc.     

Combination of Resonance and Non-Resonance Chiral Raman Scattering in a Cobalt(III) Complex

Resonance Raman optical activity (RROA) spectra with high sensitivity reveal details on molecular structure, chirality, and excited electronic properties. Despite the difficulty of the measurements, the recorded data for the Co(III) complex with S,S-N,N-ethylenediaminedisuccinic acid are of exceptional quality and, coupled with the theory, spectacularly document the molecular behavior in resonance. This includes a huge enhancement of the chiral scattering, contribution of the antisymmetric polarizabilities to the signal, and the Herzberg-Teller effect significantly shaping the spectra. The chiral component is by about one order of magnitude bigger than for an analogous aluminum complex. The band assignment and intensity profile were confirmed by simulations based on density functional and vibronic theories. The resonance was attributed to the S₀→S₃ transition, with the strongest signal enhancement of Raman and ROA spectral bands below about 800 cm⁻¹. For higher wavenumbers, other excited electronic states contribute to the scattering in a less resonant way. RROA spectroscopy thus appears as a unique tool to study the structure and electronic states of absorbing molecules in analytical chemistry, biology, and material science.     

Nickel(II) Analogues of Phosphorescent Platinum(II) Complexes with Picosecond Excited-State Decay

Square-planar Ni^II complexes are interesting as cheaper and more sustainable alternatives to Pt^II luminophores widely used in lighting and photocatalysis. We investigated the excited-state behavior of two Ni^II complexes, which are isostructural with two luminescent Pt^II complexes. The initially excited singlet metal-to-ligand charge transfer (¹MLCT) excited states in the Ni^II complexes decay to metal-centered (³MC) excited states within less than 1 picosecond, followed by non-radiative relaxation of the ³MC states to the electronic ground state within 9–21 ps. This contrasts with the population of an emissive triplet ligand-centered (³LC) excited state upon excitation of the Pt^II analogues. Structural distortions of the Ni^II complexes are responsible for this discrepant behavior and lead to dark ³MC states far lower in energy than the luminescent ³LC states of Pt^II compounds. Our findings suggest that if these structural distortions could be restricted by more rigid coordination environments and stronger ligand fields, the excited-state relaxation in four-coordinate Ni^II complexes could be decelerated such that luminescent ³LC or ³MLCT excited states become accessible. These insights are relevant to make Ni^II fit for photophysical and photochemical applications that relied on Pt^II until now.     

Relativistic effects in spectroscopy and photophysics of heavy-metal complexes illustrated by spin–orbit calculations of [Re(imidazole)(CO)3(phen)]+

Spin–orbit coupling (SOC) is an essential factor in photophysics of heavy transition metal complexes. By enabling efficient population of the lowest triplet state and its strong emission, it gives rise to a very interesting photophysical behavior and underlies photonic applications such as organic light emitting diodes (OLED) or luminescent imaging agents. SOC affects excited-state characters, relaxation dynamics, radiative and nonradiative decay pathways, as well as lifetimes and reactivity. We present a new photophysical model based on mixed-spin states, illustrated by relativistic spin–orbit TDDFT and MS-CASPT2 calculations of [Re(imidazole)(CO)₃(1,10-phenanthroline)]⁺. An excited-state scheme is constructed from spin–orbit (SO) states characterized by their energies, double-group symmetries, parentages in terms of contributing spin-free singlets and triplets, and oscillator strengths of corresponding transitions from the ground state. Some of the predictions of the relativistic SO model on the number and nature of the optically populated and intermediate excited states are qualitatively different from the spin-free model. The relativistic excited-state model accounts well for electronic absorption and emission spectra of Re^I carbonyl diimines, as well as their complex photophysical behavior. Then, we discuss the SO aspects of photophysics of heavy metal complexes from a broader perspective. Qualitative SO models as well as previous relativistic excited-state calculations are briefly reviewed together with experimental manifestations of SOC in polypyridine and cyclometallated complexes of second- and third row d⁶ metals. It is shown that the relativistic SO model can provide a comprehensive and unifying photophysical picture.     

Excited state properties from the equations of motion method. Application of the MCTDHF-MCRPA to the dipole moments and oscillator strengths of the A 1Π, a′3Π, a′3Σ+ and d3Δ low-lying valence states of CO

By examining the exact operator O_λ⁺ which is the solution of the equations of motion-Green's function method, we rederive expressions for non-reference (usually excited) state properties. Hence, additional useful information such as state expectation values, oscillator strengths, and frequency dependent and independent polarizabilities may be easily obtained from an equation of motion-Green's function calculation. With the multiconfigurational random phase approximation (MCRPA), which is equivalent to the multiconfigurational time dependent Hartree-Fock (MCTDHF), excitation energies, oscillator strengths, and excitation operators from the ground states are obtained for the low-lying valence (under 10 eV above the ground state) states of CO at the experimental ground state equilibrium geometry. We apply these techniques to obtain the excited state dipole moments for and oscillator strengths between the A ¹Π, a ³Π, a′ ³Σ⁺, and d ³Δ states of CO and compare our results to other calculations and experiments.     

Theoretical investigations of the electronic states of porphyrins. II. Normal and hyper phosphorus porphyrins

Ab initio methods have been used to calculate the ground and excited states of “normal” and “hyper” porphyrins. Perturbation theory and CI methods were used to determine differential ground and excited-state correlation effects for [P^v(P)F₂]⁺ and [P^III(P)]⁺. A comparison is made to the INDO /S /CI predicted wavefunctions and spectra and to the experimental spectra of closely related molecules. The “hyper” [P^III(P)]⁺ calculations show some very low energy electronic transitions which provide an explanation for an anomalous “red” band in the spectrum and for the lack of fluorescence. Ab initio calculations also predict that (1) the lowest energy ¹A₁ state is a two-configuration wavefunction which can be described as a diradical, (2) the two lowest-energy singlet excited states are double excitations from the closed shell SCF configuration, and (3) a ³B₂ state is very close in energy to the lowest ¹A₁ state.