Anharmonicity of a molecular oscillator

The phenomenon of anharmonicity has been proved to be an effect of coupling between the change of nuclear positions in molecular vibrations ( Q ) and the electronic degrees of freedom as represented by the chemical potential (μ) at constant number of electrons (N). The coupling parameters have well‐founded meaning in the conceptual density functional theory (DFT), first approximations to their numerical values have recently become available. The effect of coupling between normal vibrational modes also appears to be the direct consequence of the electron‐nuclear coupling. To show the pure anharmonic effect, calculations for a collection of diatomic molecules have been presented. The anharmonicity, described in the present work as d³E/d Q ³ ≠ 0, has been proved to be the intrinsic property of every oscillating molecular system. A small anharmonic contribution exists even for the “strong harmonic” oscillator, when for the force constant k both a = (?k/? Q )_N = 0 and λ = (?k/?N) _Q = 0. The latter derivative of the force constant appears to be primary factor determining the anharmonic property of a molecule. An estimate of its values has been provided from the experimental data on the anharmonicity of diatomic molecules. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

Slowing down of oxygen migration in the processes of radical oxidation and of phenanthrene phosphorescence quenching in methanol glasses at 90 K

The hydroxymethyl radical oxidation kinetics follows the second-order equation with a time-dependent rate constant, K(t). The annealing effect is described by way of dividing K(t) into two factors, one of them depending on the preliminary annealing time (τ): K(t) = K₁(t + τ)K₂(t). The time dependence of both factors is fairly well approximated by the power functions: K₁(t + τ) ≈ (t + τ)^−0.18 and K₂(t ≈ t^−0.26. The oxygen quenching of phenanthrene phosphorescence follows an exchange mechanism, with the static conditions setting in at 77 K. At 90 K oxygen diffusion adds to the quenching efficiency. The time of oxygen jumps (τ_j) and its time dependence under the matrix annealing at 90 K are determined by comparing the theoretical 1/τ_j dependence of the quenching volume with experiment. The 1/τ_j(τ) is well described by the power function τ^{−0.18 ± 0.02)}. The annealing time functions of the oxidation rate constant and of the inverse jumping time are similar. The oxidation rate constant and the diffusion constant coincide in the order of magnitude. Consequently, the slowing down of oxygen migration contributes essentially to the time dependence of the rate constant.     

Fluorescence spectra and intramolecular vibrational redistribution in jet-cooled perylene

The jet-cooled fluorescence spectra of perylene excited to the S₁ state with E_vib = 0–1600 cm^?1 are recorded and analyzed. For E_vib <800 cm^?1 only the resonant fluorescence was detected. Ground- and excited-state frequencies of 14 low-frequency normal modes are determined. A drastic change in frequency of the “butterfly” modes upon electronic excitation shows that perylene slightly deviates from planarity in its ground state and is more rigid in the excited singlet state. For a number of levels in the E_vib = 800–1600 cm^?1 range, the fluorescence is composed of the resonant emission and of non-resonant (“‘relaxed’”) bands. It is shown that apparently single bands in the fluorescence-excitation spectrum correspond to ovelapping bands pumping different molecular eigenstates resulting from the intrastate coupling. The relative role of the anharmonicity and of the Coriolis interaction are discussed. The data are treated in terms of a selective coupling between doorway and hallway states with the coupling constant rapidly decreasing with the difference in the overall vibrational quantum number between initial and final state.     

OH自由基的高精度量子化学研究

采用内收缩MRCI方法(Internally Contracted Multiconfiguration-Reference Configuration Interaction)研究了OH自由基, 计算得到其基态稳定构型的键长是0.09708 nm, 对应的实验值是0.096966 nm, 第一激发态的键长是0.10137 nm,实验值是0.10121 nm. 同时得到势能曲线PECs (Potential Energy Curve), 再分别由Murrell-Sorbie势能函数拟合计算和POLFIT程序计算得到OH自由基在基态X²Π和第一激发态A²Σ⁺时的光谱数据：平衡振动频率ω_e, 非谐性常数ω_eχ_e以及高阶修正ω_eY_e, 平衡转动常数B_e, 振转耦合系数α_e, 解离能D₀和垂直跃迁能量ν₀₀. 这些理论计算结果与最新的实验值非常吻合, 精确度比前人也有很大提高. 其中我们计算得到基态OH(X²Π)的解离能D₀＝35568.86 cm^－1, 第一激发态OH (A²Σ⁺)的解离能D₀＝18953.93 cm^－1, 从第一激发态A²Σ⁺ (ν＝0)到基态X²Π (v＝0)的垂直跃迁能ν₀₀＝32496.42 cm^－1.     

Tunneling dynamics of one- and two-dimensional cubic oscillators with randomly fluctuating harmonic force constants: A numerical experiment

The tunneling dynamics of one- and two-dimensional cubic oscillators having randomly fluctuating harmonic force constants (K_t) are studied numerically by invoking the time-dependent Fourier grid Hamiltonian method. The influence of the frequency and strength of the fluctuation on the tunneling probability and tunneling rate is analyzed. The predicted nature of the influence depends upon whether the cubic oscillator is one- or two-dimensional. The possibility of mapping the proton-transfer systems onto the present model is explored. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 64 : 403–409, 1997     

Time-Dependent Density Matrix Renormalization Group Coupled with n-Mode Representation Potentials for the Excited State Radiationless Decay Rate: Formalism and Application to Azulene?

We propose a method for calculating the nonradiative decay rates for polyatomic molecules including anharmonic effects of the potential energy surface (PES) in the Franck-Condon region. The method combines the n-mode representation method to construct the ab initio PES and the nearly exact time-dependent density matrix renormalization group method (TD-DMRG) to simulate quantum dynamics. In addition, in the framework of TD-DMRG, we further develop an algorithm to calculate the final-state-resolved rate coefficient which is very useful to analyze the contribution from each vibrational mode to the transition process. We use this method to study the internal conversion (IC) process of azulene after taking into account the anharmonicity of the ground state PES. The results show that even for this semi-rigid molecule, the intramode anharmonicity enhances the IC rate significantly, and after considering the two-mode coupling effect, the rate increases even further. The reason is that the anharmonicity enables the C-H vibrations to receive electronic energy while C-H vibrations do not contribute on the harmonic PES as the Huang-Rhys factor is close to 0.     

Femtosecond dynamics of excited-state intramolecular proton transfer in <Emphasis Type="Italic">o</Emphasis>-tosylaminobenzaldehyde

Dynamics of excited-state intramolecular proton transfer (ESIPT) in o-tosylaminobenzaldehyde has been studied by femtosecond absorption spectroscopy with a time resolution of 30 fs. The characteristic time of this process is ∼100 fs. Differential absorption rate curves exhibit oscillations that are consistent with theoretically predicted ESIPT-promoting vibrational modes. Efficient nonradiative deactivation with a rate constant of 6.25 × 10¹⁰ s⁻¹ occurs in the excited product of proton transfer, with internal rotation followed by intersystem crossing being one of the feasible deactivation pathways.     

Nonadiabatic coupling and diabatic electronic population dynamics on 11A2 and 11B1 states of ozone molecule

In this work, we examine nonadiabatic population dynamics for 1¹B₁ and 1¹A₂ states of ozone molecule (O₃). In O₃, two lowest singlet excited states, ¹A₂ and ¹B₁, can be coupled. Thus, population transfer between them occurs through the seam involving these two states. At any point of the seam (conical intersection), the Born-Oppenheimer approximation breaks down, and it is necessary to investigate nonadiabatic dynamics. We consider a linear vibronic coupling Hamiltonian model and evaluate vibronic coupling constant, diabatic frequencies for three modes of O₃, bilinear and quadratic coupling constants for diabatic potentials, displacements, and Huang-Rhys coupling constants using ab initio calculations. The electronic structure calculations have been performed at the multireference configuration interaction and complete active space with second-order perturbation theory with a full-valence complete active space self-consistent field methods and augmented Dunning's standard correlation-consistent-polarized quadruple zeta basis set to determine ab initio potential energy surfaces for the ground state and first two excited states of O₃, respectively. We have chosen active space comprising 18 electrons distributed over 12 active orbitals. Our calculations predict the linear vibronic coupling constant 0.123 eV. We have obtained the population on the 1¹B₁ and 1¹A₂ excited electronic states for the first 500 fs after photoexcitation.     

Theoretical study of the polarized infrared spectra of the hydrogen bond in 2‐furoic acid crystal dimer

This work presents a theoretical simulation of ν_{O? H} and ν_{O? D} band shapes in the polarized infrared spectra of 2‐furoic acid dimer crystals measured at liquid‐nitrogen temperature. The line shapes are studied theoretically within the framework of the anharmonic couplings between low‐frequency hydrogen‐bond vibrations and degenerate excited states of high‐frequency hydrogen vibrations in hydrogen‐bonded dimers and the anharmonic coupling between the first excited state of the fast mode and the harmonics or band combinations of some low‐frequency bending modes, which lead to Fermi resonances.This approach takes into account the adiabatic approximation, the intrinsic anharmonicity of the low‐frequency mode through a Morse potential, Davydov coupling triggered by resonance exchange between the excited states of the fast modes of the two hydrogen bonds involved in the cyclic dimer, and the direct and indirect damping of the fast‐stretching modes of the hydrogen bonds and of the bending modes. The infrared spectral density was calculated within the linear response theory by Fourier transform of the autocorrelation function of the transition dipole moment operator of the fast mode. Numerical results show that mixing of all these effects allows satisfactory reproduction of the main features of the experimental IR line shapes of crystalline H‐ and D‐bonded 2‐furoic acid at liquid‐nitrogen temperature and for different polarizations. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Fluorescence quenching of para-substitutedstyrenes by tetramethylethylene. Correlationanalysis of the quenching coefficient KSV and thequenching rate constant k_q by the dual-parameter equation with polar and spin-delocalization substituent constants

The fluorescence quenching coefficient (Ksv) and the quenching rate constant kq of ten para-substituted styrenes (1-Ys) have been measured and correlation-analyzed by both the dual-parameter equation (Eq. 1) with (ρxσx+ρ'σ') and the single-parameter equation (Eq. 2) with ρxσx. Ex-cellent results have been obtained for the correlation of KSV against (ρxσmb+ρ'σ'JJ) or (ρxσ+ +ρ'σ'JJ). Our results suggest that, possibly, there might be no need to use excited-state substituent constant for the fluorecence quenching process of excited states of styrenes.     

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.     

Comparison of Phosphorescent Pt(II) Complexes with C^N^N vs N^N^N Chelators and Caffeine-Based NHC-co-ligands†

In this work, we explored coordination compounds featuring caffeine-based carbene co-ligands and tridentate dianionic pincer luminophores derived from 2,6-bis(1H-1,2,4-triazol-5-yl)pyridine (N), as well as from 2-phenyl-6-(1H-1,2,4-triazol-5-yl)pyridine (C), bearing either Ad (adamantyl) or tBu (tertiary butyl) substituents. The new 2-phenyl-6-(1H-1,2,4-triazol-5-yl)pyridine-based ligand precursors along with four Pt(II) complexes, namely Pt(C-tBu), Pt(C-Ad), Pt(N-tBu) and Pt(N-Ad) were characterized. Further on, the influence of the different substituents at the chelating luminophores and of the caffeine-based NHC-co-ligand on the photophysical properties (including photoluminescence quantum yields (Φ_L), excited-state lifetimes (τ), radiative (k_r), and non-radiative (k_nr) deactivation rate constants) was assessed in fluid solutions at room temperature (RT) and in frozen glassy matrices at 77 K. All four luminophores perform equivalently well within the experimental uncertainty. In deoxygenated fluid solutions at RT, photoluminescence quantum yields reaching up to 24 ± 2% and excited-state lifetimes of around 12 μs were found. The generally long excited-state lifetimes and only minor blue shift upon cooling to 77 K along with mostly well-resolved vibrational progressions point to metal-perturbed ligand-centered excited states. Notably, the yield of the complexation reaction in case of Pt(C-tBu) and Pt(C-Ad) was almost two times higher compared to Pt(N-tBu) and Pt(N-Ad). Cyclometallation is not an essential feature to achieve high photoluminescence quantum yields, but it can improve the synthetic efficiency. In summary, it can be observed that coordination chemical concepts based on natural products can lead to stable phosphorescent species with interesting excited-state properties.     

Excited states of OsO4: A comprehensive time‐dependent relativistic density functional theory study

A large number of scalar as well as spinor excited states of OsO₄, in the experimentally accessible energy range of 3–11 eV, have been captured by time‐dependent relativistic density functional linear response theory based on an exact two‐component Hamiltonian resulting from the symmetrized elimination of the small component. The results are grossly in good agreement with those by the singles and doubles coupled‐cluster linear response theory in conjunction with relativistic effective core potentials. The simulated‐excitation spectrum is also in line with the available experiment. Furthermore, combined with detailed analysis of the excited states, the nature of the observed optical transitions is clearly elucidated. It is found that a few scalar states of ³T₁ and ³T₂ symmetries are split significantly by the spin‐orbit coupling. The possible source for the substantial spin‐orbit splittings of ligand molecular orbitals is carefully examined, leading to a new interpretation on the primary valence photoelectron ionization spectrum of OsO₄. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

PHOTOPHYSICS OF THE FLUORESCENT Ca2+ INDICATOR QUIN-2

The photophysics of the complex forming reaction between Quin-2 and Ca²⁺ were investigated using steady-state and time-resolved fluorescence measurements. The fluorescence decay traces were analyzed with global compartmental analysis yielding the following values for the rate constants at room temperature in aqueous solution with EGTA as Ca²⁺ buffer: k₀₁= 8.6 times 10⁸ s^?1, k₂₁= 1 times 10¹¹M^?1 s^?1, k₀₂= 8.8 times 10⁷ s^?1, k₁₂= 4 times 10⁴ s^?1. k₀₁ and k₀₂ denote the respective deactivation rate constants of the Ca²⁺ free and bound forms of Quin-2 in the excited state. The constant k₂₁ represents the second-order rate constant of binding of Ca²⁺ and Quin-2 in the excited state while k₁₂ is the first-order rate constant of dissociation of the excited Ca²⁺:Quin-2 complex. From the estimated values of k₁₂ and k₂₁ the dissociation constant K_d* in the excited state was calculated. It was found that pK_d* (6.4) is slightly smaller than pK_d (7.2). There was no interference of the excited-state complex forming reaction with the determination of K_d. Intracellular Ca²⁺ concentrations can thus accurately be determined from fluorometric measurements using Quin-2 as Ca²⁺ indicator.     

Vibrational anharmonicity effects in electronic tunneling through molecular bridges

Effects of anharmonic bridge vibrations on electronic tunneling in donor-bridge-acceptor complexes are studied using a model of anharmonic bridge vibration coupled nonlinearly to an electronic degree of freedom. An anharmonicity parameter is introduced, enabling to reproduce the standard harmonic model with linear coupling as a limiting case. The frequency of electronic tunneling oscillations between the donor and acceptor sites is shown to be sensitive to the nuclear anharmonicity, where stretching and compression modes have an opposite effect on the electronic frequency. This phenomenon, that cannot be accounted for within the harmonic approximation, is analyzed and explained.     

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⁺.     

Benchmark calculations for dissipative dynamics of a system coupled to an anharmonic bath with the multiconfiguration time-dependent Hartree method

In this paper, we present benchmark results for dissipative dynamics of a harmonic oscillator coupled to an anharmonic bath of Morse oscillators. The microscopic Hamiltonian has been chosen so that the anharmonicity can be adjusted as a free parameter, and its effect can be isolated. This leads to a temperature dependent spectral density of the bath, which is studied for ohmic and lorentzian cases. Also, we compare numerically exact multiconfiguration time-dependent Hartree results with approximate solutions using continuous configuration time-dependent self-consistent field and local coherent state approximation.     

From chemical structure to viscoelastic properties of polymers

The basic result of the coupling model consists of a cross-over from exp-(t/τ_o) to exp-(t/τ*)^1-n at a temperature insensitive microscopic time t_c. We indicate how this basic result can be derived from chaotic, interacting Hamiltonian systems which include densely packed polymer molecules. Recent quasielastic neutron scattering experiments and molecular dynamics simulations are discussed and the results are shown to support this result as well. An application of the coupling model to find how the viscoelasticity of a polymer depends on the chemical structure of the monomer through the coupling parameter of the local segmental motion is given to illustrate the utility of the model.     

Pseudorotational dynamics of H3+ and Li3+

The origin of the pseudoprecession phenomenon is investigated through a computational study of the time evolution of H₃⁺ and Li₃⁺ by electron nuclear dynamics theory. In particular, the pseudorotation of both molecules is shown to induce a spatial rotation, which in turn leads to Coriolis coupling of the two orthogonal nuclear shape deformation modes. This effect is rooted in an anisotropy of the molecular ground state potential energy surface that is caused by the interaction between the D_3h ground state and a twofold degenerate first excited state. Computations are performed for a variety of vibrational energies. In addition, the impact of the anharmonicity of the ground state potential surface on the shape deformation modes and the coupling between them is discussed. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

First principles calculation of the thermodynamic properties of silicon clusters

The thermodynamic properties of Si clusters are calculated using first principles quantum methods combined with molecular dynamics for simulating the trajectories of clusters. A plane wave basis is used with ab initio pseudo potentials and the local density approximation for determining the electronic energies and forces. Langevin molecular dynamics simulates thermal contact with a constant temperature reservoir. Vibrational spectra, moments of inertia, anharmonic corrections, and free energies are predicted for Si₂ through Si₅. The translational contribution is based on the ideal gas limit. The rotation contribution is approximated using a classical rigid rotator. Vibrational modes are determined from the dynamical matrix in the harmonic approximation. Corrections due to anharmonicity and coupling between rotational and vibrational modes are fit from the molecular dynamics simulations. Received: 17 September 1997 / Accepted: 14 October 1997