Toward quantitative prediction of molecular fluorescence quantum efficiency: role of duschinsky rotation

It is a highly desirable but difficult task to predict the molecular fluorescence quantum efficiency from first principles. The molecule in the excited state can undergo spontaneous radiation, conversion of electronic energy to nuclear motion, or chemical reaction. For relatively large molecules, it is impossible to obtain the full potential energy surfaces for the ground state and the excited states to study the excited-state dynamics. We show that, under harmonic approximation by considering the Duschinsky rotation effect, the molecular fluorescence properties can be quantitatively calculated from first principles coupled with our correlation function formalism for the internal conversion. In particular, we have explained the peculiar fluorescence behaviors of two isomeric compounds, cis,cis-1,2,3,4-tetraphenyl-1,3-butadiene and 1,1,4,4-tetraphenyl-butadiene, the former being nonemissive in solution and strongly emissive in aggregation or at low temperature, and the latter being strongly emissive in solution. The roles of low-frequency phenyl ring twist motions and their Duschinsky mode mixings are found to be crucial, especially to reveal the temperature dependence. As an independent check, we take a look at the well-established photophysics of 1,4-diphenylbutadiene for its three different conformers. Both the calculated radiative and nonradiative rates are in excellent agreement with the available experimental measurements.     

Promoting-mode free formalism for excited state radiationless decay process with Duschinsky rotation effect

In the present work, through the path integral of Gaussian type correlation function, a new formalism based on Fermi-Golden Rule for calculating the rate constant of nonradiative decay process with Duschinsky rotation effect in polyatomic molecules is developed. The advantage of the present path-integral formalism is promoting-mode free. In order to get the rate constant, a "transition rate matrix" needs to be calculated. The rate constant calculated previously is only an approximation of diagonal elements of our "transition rate matrix " . The total rate should be the summation over all the matrix elements.     

Laser cooling of vibrational degrees of freedom of a molecular system

We consider the cooling of vibrational degrees of freedom in a photoinduced excited electronic state of a model molecular system. For the various parameters of the potential surfaces of the ground and excited electronic states and depending on the excitation frequency of a single-mode laser light, the average energy or average vibrational temperature of the excited state passes through a minimum. The amount of cooling is quantified in terms of the overlap integral between the ground and excited electronic states of the molecule. We have given an approach to calculate the Franck-Condon factor for a multimode displaced-distorted-rotated oscillator surface of the molecular system. This is subsequently used to study the effect of displacement, distortion, and Duschinsky rotation on the vibrational cooling in the excited state. The absorption spectra and also the average energy or the effective temperature of the excited electronic state are studied for the above model molecular system. Considering the non-Condon effect for the symmetry-forbidden transitions, we have discussed the absorption spectra and average temperature in the excited-state vibrational manifold.     

位移谐振子模型对三(2-苯基吡啶)合铱磷光光谱影响的理论研究

采用谐振子模型理论探讨了振动模式对Ir(ppy)₃配合物的磷光光谱的影响.多原子分子发射光谱的一般形式可以从两个绝热电子态之间的热振动关联函数推导出,相应地势能面之间的位移和Duschinsky转动的影响也被包含在多维谐振子模型的表达式中,所得关系式模拟出了Ir(ppy)₃较为精细的磷光发射光谱.计算结果表明T₁态到S₀态之间的0→1振动跃迁对发射光谱贡献较大,尤其振动频率小于1600 cm^-1的振动模贡献更多,配体中苯和吡啶环上C=C和C=N的呼吸振动,是Ir(ppy)₃出现肩峰的主要原因.玻耳兹曼分布使得主峰和肩峰的强度下降,并且两峰相互接近.该谐振子模型与密度泛函理论(DFT)结合,可以较好地定量描述多原子分子光物理过程的发射光谱以及详细了解光谱谱图的细节.     

Adiabatic passage by light-induced potentials in polyatomic molecules

In this paper we study the first application of adiabatic passage by light-induced potentials in polyatomic molecules. We analyze the effects of increasing the dimensionality of the system on the adiabatic requirements of the method and the role of intramolecular coupling among the vibrational modes. By using a model of two-dimensional displaced harmonic oscillators with or without rotation of the normal mode axis of the excited states (Duschinsky effect) we find that (1) it is possible to selectively transfer the vibrational population by adiabatic elongation of the bonds, (2) the adiabatic demands depend mainly on the energy barrier between the ground and excited electronic configurations, and not on the dimension of the system, (3) in the presence of intramolecular couplings the selective transfer can be achieved but at the cost of increasing the duration and/or the intensity of the pulses, which are needed to overcome small avoided crossings, and (4) the problem of selectivity becomes more important as the vibrational energy of the initial wave function increases.     

Resonance Raman spectra of uracil based on Kramers-Kronig relations using time-dependent density functional calculations and multireference perturbation theory

The use of time-dependent density functional calculations for the optimization of excited-state structures and the subsequent calculation of resonance Raman intensities within the transform-theory framework is compared to calculations of Hartree-Fock/configuration interaction singles-type (CIS). The transform theory of resonance Raman scattering is based on Kramers-Kronig relations between polarizability tensor components and the optical absorption. Stationary points for the two lowest excited singlet states of uracil are optimized and characterized by means of numerical differentiation of analytical excited-state gradients. It is shown that the effect of electron correlation leads to substantial modifications of the relative intensities. Calculations of vibrational frequencies for ground and excited states are carried out, which show that the neglect of Duschinsky mixing and the assumption of equal wave numbers for ground and excited state are not in all cases good approximations. We also compare the transform-theory resonance Raman intensities with those obtained within a simple approximation from excited-state gradients at the ground-state equilibrium position, and find that they are in qualitative agreement in the case of CIS, but show some important differences in calculations based on density functional theory. Since the results from CIS calculations are in better agreement with experiment, we also present approximate resonance Raman spectra obtained using excited-state gradients from multireference perturbation theory calculations, which confirm the CIS gradients.     

“Proximity effects” in radiative transitions: a model study of the role of vibronic coupling and static crystal field interactions

We report the results of a model study of the influence of vibronic coupling involving non-totally symmetric vibrations and static crystal field interactions on the spectral properties of molecules with close-lying excited electronic states. The presented results suggests that “proximity effects” brought about by solvent perturbation arise from two sources: (i) alterations in the energy separation between vibronically coupled electronic states and (ii) crystal field mixing of the isolated molecular electronic states. It is shown that crystal field mixing leads to the breakdown of the vibronic coupling scheme for non-totally symmetric vibrations in isolated molecules. This breakdown is shown to have a very pronounced effect on the spectral properties of molecules with close-lying excited electronic states. The effect of environmental perturbations on excited state frequencies, the breakdown of symmetry and polarization selection rules, and vibrational intensity distributions is discussed.     

Low-frequency vibrations specific for conformers of 1-aminoindan studied by UV-UV hole-burning spectroscopy

The UV-UV hole-burning spectra of the jet-cooled 1-aminoindan were measured for the first time. Complicated spectral features observed in the laser-induced fluorescence excitation spectrum due to two conformers, R and B, were firmly separated. On the basis of fluorescence measurements and B3LYP/cc-pVTZ calculations, low-frequency ring twisting and ring puckering modes were assigned. These modes are coupled in the S1 state due to the Duschinsky rotation. The Duschinsky matrix was calculated from the normal modes predicted by quantum chemical calculations. The coupling between the twisting and puckering modes for conformer B is stronger than that for conformer R. The twisting mode was observed at 0+99 cm(-1) in the S1 state for conformer B, while not for conformer R. The Franck-Condon activity of the twisting mode substantially differs between the two conformers. The transition to the twisting level for conformer B would be allowed by the Duschinsky rotation. The fluorescence lifetime of conformer vibronic levels was also measured and differed for each conformer.     

面向有机光电材料的电子激发态结构与过程的计算方法

共轭聚合物与有机分子材料中的电子激发结构与过程决定了材料的光电功能：根据Kasha规则,低能级激发态的排序决定能否发光;最低激发态至基态的辐射跃迁与无辐射跃迁之间的竞争决定了发光效率,后者主要由非绝热耦合（声子作用）决定;电荷激发态载体的传输由电子分布与振动耦合或杂质和无序的散射弛豫过程决定．本文针对有机功能材料的发光性能,介绍两种理论方法的研究进展,即可用于计算共轭聚合物激发态结构的量子化学密度矩阵重整化群方法和计算发光效率的多模耦合无辐射跃迁速率方法．这些方法被应用于有机功能材料的性能预测和分子设计中．     

CASSCF and CASPT2 studies on the structures, transition energies, and dipole moments of ground and excited states for azulene

The electronic structure of azulene molecule has been studied. We have obtained the optimized structures of ground and singlet excited states by using the complete active space self-consistent-field (CASSCF) method, and calculated vertical and 0-0 transition energies between the ground and excited states with second-order M?ller-Plesset perturbation theory (CASPT2). The CASPT2 calculations indicate that the bond-equalized C(2v) structure is more stable than the bond-alternating C(s) structure in the ground state. For a physical understanding of electronic structure change from C(2v) to C(s), we have performed the CASSCF calculations of Duschinsky matrix describing mixing of the b(2) vibrational mode between the ground (1A(1)) and the first excited (1B(2)) states based on the Kekule-crossing model. The CASPT2 0-0 transition energies are in fairly good agreement with experimental results within 0.1-0.3 eV. The CASSCF oscillator strengths between the ground and excited states are calculated and compared with experimental data. Furthermore, we have calculated the CASPT2 dipole moments of ground and excited states, which show good agreement with experimental values.     

General harmonic oscillator integrals by the operator method

The operator technique with a minimum of commutator algebra is employed to calculate matrix elements of any number of operators between distorted, displaced harmonic oscillator wavefunctions. The results are valid for multidimensional integrals, and regardless of the extent of the Duschinsky effect. General recursion relations useful in machine calculations are given. The formalism is illustrated for the well-known one-dimensional Franck–Condon integrals.     

Formation and relaxation of excited states in solution: a new time dependent polarizable continuum model based on time dependent density functional theory

In this paper a novel approach to study the formation and relaxation of excited states in solution is presented within the integral equation formalism version of the polarizable continuum model. Such an approach uses the excited state relaxed density matrix to correct the time dependent density functional theory excitation energies and it introduces a state-specific solvent response, which can be further generalized within a time dependent formalism. This generalization is based on the use of a complex dielectric permittivity as a function of the frequency, epsilonomega. The approach is here presented in its theoretical formulation and applied to the various steps involved in the formation and relaxation of electronic excited states in solvated molecules. In particular, vertical excitations (and emissions), as well as time dependent Stokes shift and complete relaxation from vertical excited states back to ground state, can be obtained as different applications of the same theory. Numerical results on two molecular systems are reported to better illustrate the features of the model.     

Molecular Polygons Probe the Role of Intramolecular Strain in the Photophysics of π‐Conjugated Chromophores

π‐Conjugated segments, chromophores, are the electronically active units of polymer materials used in organic electronics. To elucidate the effect of the bending of these linear moieties on elementary electronic properties, such as luminescence color and radiative rate, we introduce a series of molecular polygons. The π‐system in these molecules becomes so distorted in bichromophores (digons) that these absorb and emit light of arbitrary polarization: any part of the chain absorbs and emits radiation with equal probability. Bending leads to a cancellation of transition dipole moment (TDM), increasing excited‐state lifetime. Simultaneously, fluorescence shifts to the red as radiative transitions require mixing of the excited state with vibrational modes. However, strain can become so large that excited‐state localization on shorter units of the chain occurs, compensating TDM cancellation. The underlying correlations between shape and photophysics can only be resolved in single molecules.     

Current functional theory for multi-electron configuration

The density functional theory (DFT) formalism is reformulated into a framework of currents so as to give the energy a parameter dependent behaviour, e.g., time. This “current” method is aimed at describing the transition of electrons from one orbital to another and especially from the ground state to an excited state and extended to the relativistic region in order to include magnetic fields which is relevant especially for heavy metallic compounds. The formalism leads to a set of coupled first order partial differential equations to describe the time evolution of atoms and molecules. The application of the method to ZnO and H₂O to calculate the occupation probabilities of the orbitals lead to the results that compare favorably with those obtained from DFT. Furthermore, evolution equations for electrons in both atoms and molecules can be derived. Applications to specific examples of small molecules (being metallo-oxides and water) are mentioned at the end.