Duschinsky Rotation Research Articles

The influence of spin–orbit coupling, Duschinsky rotation and displacement vector on the rate of intersystem crossing of benzophenone and its fused analog fluorenone: a time dependent correlation function based approach

To understand the effect of structural rigidity or flexibility on the intersystem crossing rate, herein we have adopted a time dependent correlation function based approach, an appropriate method for a harmonic oscillator under Condon approximation. Following this technique, we have developed generalized codes for calculating the rate of intersystem crossing (ISC) both at 0 K and at finite temperature. Since the rate of ISC is a measurable quantity, we have separated the real and imaginary parts of the complex correlation function carefully and eliminated the imaginary part by exploiting the odd nature of this function. Using this simplified method, we have calculated the ISC rate constant (kISC) of two molecules, namely, benzophenone and its fused analog, fluorenone. The calculations clearly elucidate that kISC of benzophenone is 103 times larger compared to that of fluorenone. Interestingly, our analyses reveal that the combined effect of spin-orbit coupling and the number of normal modes could increase the rate of ISC of benzophenone by three orders in comparison to that of fluorenone. Furthermore, the Duschinsky rotation matrix (J) and displacement vectors (D) could influence the rate of ISC by one order each, indicating that the overall rate of ISC of benzophenone could have been 105 times higher than that of fluorenone if the latter two factors, namely, J and D have practically no impact on the rate of ISC of fluorenone. However, it has been found that albeit J can't alter the rate of ISC of fluorenone, D indeed can change the rate by two orders, thereby keeping the overall ratio of the rate of ISC of benzophenone and fluorenone as 103. The present study elucidates that none of the above mentioned factors alone can explain the relative rate of ISC of the studied systems; rather a complex interplay between all these factors makes the rate of ISC of benzophenone 103 times higher than that of fluorenone.

A new mechanistic study of a second generation TADF material based on the path integral approach incorporating Herzberg–Teller and Duschinsky rotation effects

Quantitative predictions of the photophysical processes for a next generation thermally activated delayed fluorescence molecule are calculated by considering the Herzberg–Teller and the Duschinsky rotation effects within a multimode harmonic oscillator model.

Theoretical study and experimental validation on the optical emission processes in "free" and "locked" pyrazine derivatives.

The excited-state properties of the "free" and "locked" pyrazine derivatives are investigated in solution. DCFP with "free" phenyls is theoretically calculated to be non-emissive due to the non-radiative energy dissipation through strong Duschinsky rotation effect, in agreement with the available experimental result. Surprisingly, DCBP with "bi-locked" phenyls is also calculated to be nonluminous. The emission of DCAP with "conjoined" architecture is predicted to be weaker than DCPP with "single-locked" phenyls, quite contrary to our intuition but further validated by the experimental measurement. The construction of four-, five- and six-membered ring respectively in DCBP, DCAP and DCPP is found to be the major structural origin for the descending relaxation energy in these "locked" systems, thus giving rise to the ascending luminescence order. Our work not only provides strategy for the molecular design of efficient organic light-emitting materials, but also offers valuable insight into the aggregation-induced emission phenomena.

Efficient simulation of overtones and combination bands in resonant Raman spectra.

In this work, we describe how Resonant Raman (RR) spectra can be predicted with good accuracy using the path integral formulation for the harmonic oscillator, including the Herzberg-Teller and Duschinsky rotation effects. In particular, we will focus on approximations to make these calculations more efficient and expand the current methodology to include overtones and combination bands in the final prediction. After outlining the theory, we explain how it can be made into a black-box method and discuss the approximations that rely on its intrinsic parameters. It is shown that the latter can improve the efficiency by orders of magnitude, without substantial loss in accuracy. We will also show that the predicted RR spectra are in good agreement with experiment for both the intensity and position of spectral peaks, even for higher order vibronic excitations. Thus, the method proposed here can be used as a computational aid to experiments to improve the quality of analysis and theoretical understanding of RR.

On the spectral profile change in the Q band absorption spectra of metalloporphyrins (Mg, Zn, and Pd): A first-principles study.

We performed a systematic study of the vibrationally resolved absorption spectra in the Q band of three metalloporphyrins (Mg, Zn, and Pd) to understand the spectral changes in this series, including both the Franck-Condon (FC) and Herzberg-Teller (HT) contributions. The ground (S0) and the lowest singlet excited (S1) states were, respectively, simulated by the static and time-dependent density functional theory, with which the Duschinsky rotation effect was considered. Different functionals and basis sets were tested and compared with experiment. Results show that the long-range corrected functional CAM-B3LYP can nicely describe the spectral fingerprints of these metalloporphyrins, while the B3LYP functional significantly underestimates the FC contributions. We found that the absorption fine structures of these molecules are mainly caused by the HT vibronic couplings. The experimentally observed enhancements to the on-site 0-0 absorption peak in the series of Mg, Zn, and Pd are nicely reproduced. Enhanced absorption intensity is caused by larger FC contributions of molecules with heavier metal ions. The structure-spectroscopy relationship was analyzed, and it was found that the smaller cavity size of the porphyrin ring can significantly enhance the oscillator strength of the S0 → S1 transition.

Detailed analysis of the vibronic structure of phenetole in its first excited state and ionic ground state.

The vibronic structure of the first electronically excited state S1 and ionic ground state D0 of phenetole has been investigated by means of resonance enhanced multi photon ionization (REMPI) and mass analyzed threshold ionization (MATI) spectroscopy. The vibronic levels were assigned with the aid of quantum chemical calculations at the (TD)DFT level of theory and a multidimensional Franck-Condon approach. The S1 excitation energy of phenetole has been determined to be 36370 ± 4 cm-1 (4.5093 ± 0.0005 eV). The adiabatic ionization energy was determined to be 65665 ± 7 cm-1 (8.1415 ± 0.0008 eV). The vibronic structure has been analyzed whereby the in-plane bending vibration νbend shows high activity in the first excited state but is more pronounced in the ionic ground state. Moreover, a strong Duschinsky rotation effect can be observed for several D0←S1 transitions that causes violations of the Δv = 0 propensity rule.

Vibrationally resolved electronic spectra including vibrational pre-excitation: Theory and application to VIPER spectroscopy.

Vibrationally resolved electronic absorption spectra including the effect of vibrational pre-excitation are computed in order to interpret and predict vibronic transitions that are probed in the Vibrationally Promoted Electronic Resonance (VIPER) experiment [L. J. G. W. van Wilderen et al., Angew. Chem., Int. Ed. 53, 2667 (2014)]. To this end, we employ time-independent and time-dependent methods based on the evaluation of Franck-Condon overlap integrals and Fourier transformation of time-domain wavepacket autocorrelation functions, respectively. The time-independent approach uses a generalized version of the FCclasses method [F. Santoro et al., J. Chem. Phys. 126, 084509 (2007)]. In the time-dependent approach, autocorrelation functions are obtained by wavepacket propagation and by the evaluation of analytic expressions, within the harmonic approximation including Duschinsky rotation effects. For several medium-sized polyatomic systems, it is shown that selective pre-excitation of particular vibrational modes leads to a redshift of the low-frequency edge of the electronic absorption spectrum, which is a prerequisite for the VIPER experiment. This effect is typically most pronounced upon excitation of modes that are significantly displaced during the electronic transition, such as ring distortion modes within an aromatic π-system. Theoretical predictions as to which modes show the strongest VIPER effect are found to be in excellent agreement with experiment.

Theoretical studying of basic photophysical processes in a thermally activated delayed fluorescence copper(I) complex: Determination of reverse intersystem crossing and radiative rate constants

Abstract The photophysical properties of a mononuclear Cu(dppb)(pz2Bph2) complex have been investigated by employing the thermal vibration correlation function (TVCF) approach. The harmonic oscillator model with origin displacement, distortion, and Duschinsky rotation effects for the potential energy surfaces are considered. Absorption spectrum obtained by the scalar relativistic density functional theory combined with restricted open-shell configuration interaction including spin-orbit coupling effects is in excellent agreement with the experimental data. We found that the intersystem crossing (ISC) from the first excited singlet state (S1) to the triplet state (T1) is forbidden by direct spin-orbit coupling at the first-order perturbation, but becomes allowed through combined with vibronic coupling. The reverse intersystem crossing (RISC) proceeds at a rate of KRISC = 3.98 × 108 s−1 at room temperature 300 K, which is about 6 order of magnitude larger than the mean phosphorescence rate, KP, av = 7.3 × 102 s−1. At the same time, the ISC rate KISC = 3.06 × 109 s−1 is again about 3 order of magnitude larger than the fluorescence rate KF = 6.47 × 106 s−1. This implies that the S1 state can be populated from the T1 state, TADF should be observed and TADF decay time is τ(300 K) = 2.32 μs by fitting calculation. But at 30 K, the situation will change. The RISC rate becomes very small, about KRISC = 1.19 × 101 s−1, while the ISC rate only decreases slightly from KISC = 3.06 × 109 s−1 to KISC = 1.93 × 109 s−1. As a consequence, the Cu(dppb)(pz2Bph2) complex is highly attractive candidates for applications of TADF.

Vibronic Boson Sampling: Generalized Gaussian Boson Sampling for Molecular Vibronic Spectra at Finite Temperature

Molecular vibroic spectroscopy, where the transitions involve non-trivial Bosonic correlation due to the Duschinsky Rotation, is strongly believed to be in a similar complexity class as Boson Sampling. At finite temperature, the problem is represented as a Boson Sampling experiment with correlated Gaussian input states. This molecular problem with temperature effect is intimately related to the various versions of Boson Sampling sharing the similar computational complexity. Here we provide a full description to this relation in the context of Gaussian Boson Sampling. We find a hierarchical structure, which illustrates the relationship among various Boson Sampling schemes. Specifically, we show that every instance of Gaussian Boson Sampling with an initial correlation can be simulated by an instance of Gaussian Boson Sampling without initial correlation, with only a polynomial overhead. Since every Gaussian state is associated with a thermal state, our result implies that every sampling problem in molecular vibronic transitions, at any temperature, can be simulated by Gaussian Boson Sampling associated with a product of vacuum modes. We refer such a generalized Gaussian Boson Sampling motivated by the molecular sampling problem as Vibronic Boson Sampling.

Simulation of the photodetachment spectrum of HHfO- using coupled-cluster calculations.

The photodetachment spectrum of HHfO- was simulated using restricted-spin coupled-cluster single-double plus perturbative triple {RCCSD(T)} calculations performed on the ground electronic states of HHfO and HHfO-, employing basis sets of up to quintuple-zeta quality. The computed RCCSD(T) electron affinity of 1.67 ± 0.02 eV at the complete basis set limit, including Hf 5s25p6 core correlation and zero-point energy corrections, agrees well with the experimental value of 1.70 ± 0.05 eV from a recent photodetachment study [X. Li et al., J. Chem. Phys. 136, 154306 (2012)]. For the simulation, Franck-Condon factors were computed which included allowances for anharmonicity and Duschinsky rotation. Comparisons between simulated and experimental spectra confirm the assignments of the molecular carrier and electronic states involved but suggest that the experimental vibrational structure has suffered from poor signal-to-noise ratio. An alternative assignment of the vibrational structure to that suggested in the experimental work is presented.

Importance of Vibronic Effects in the UV-Vis Spectrum of the 7,7,8,8-Tetracyanoquinodimethane Anion.

We present a computational method for simulating vibronic absorption spectra in the ultraviolet-visible (UV-vis) range and apply it to the 7,7,8,8-tetracyanoquinodimethane anion (TCNQ-), which has been used as a ligand in black absorbers. Gaussian broadening of vertical electronic excitation energies of TCNQ- from linear-response time-dependent density functional theory produces only one band, which is qualitatively incorrect. Thus, the harmonic vibrational modes of the two lowest doublet states were computed, and the vibronic UV-vis spectrum was simulated using the displaced harmonic oscillator approximation, the frequency-shifted harmonic oscillator approximation, and the full Duschinsky formalism. An efficient real-time generating function method was implemented to avoid the exponential complexity of conventional Franck-Condon approaches to vibronic spectra. The obtained UV-vis spectra for TCNQ- agree well with experiment; the Duschinsky rotation is found to have only a minor effect on the spectrum. Born-Oppenheimer molecular dynamics simulations combined with calculations of the electronic excitation energies for a large number of molecular structures were also used for simulating the UV-vis spectrum. The Born-Oppenheimer molecular dynamics simulations yield a broadening of the energetically lowest peak in the absorption spectrum, but additional vibrational bands present in the experimental and simulated quantum harmonic oscillator spectra are not observed in the molecular dynamics simulations. Our results underline the importance of vibronic effects for the UV-vis spectrum of TCNQ-, and they establish an efficient method for obtaining vibronic spectra using a combination of linear-response time-dependent density functional theory and a real-time generating function approach.

Mass spectral decomposition mechanisms of RDX isomers upon electron attachment and electron ionisation: a DFT study of normal mode activation incorporating Duschinsky rotations

ABSTRACTThe excited normal modes of RDX isomers upon loss and gain of an electron were calculated using DFT methods. Isomerisation and N−N bond dissociation accompany the cation and anion formation, respectively, resulting in rather large (0.03–2.5 eV) reorganisation energies, frequency shifts and mode mixing. All active vibrations are found to be anharmonic. The suggested mass spectral fragmentation products for the cations along the S0 surface are 42, 60, 74, 84, 120, 130, 148 and 176 amu, in agreement with earlier mass spectrometry studies. For anions, N−N bond dissociation is common and dominant for all isomers with frequency shifts being more significant than mode mixing.

Simulation of the single-vibronic-level emission spectra of HAsO and DAsO.

The single-vibronic-level (SVL) emission spectra of HAsO and DAsO have been simulated by electronic structure/Franck-Condon factor calculations to confirm the spectral molecular carrier and to investigate the electronic states involved. Various multi-reference (MR) methods, namely, NEVPT2 (n-electron valence state second order perturbation theory), RSPT2-F12 (explicitly correlated Rayleigh-Schrodinger second order perturbation theory), and MRCI-F12 (explicitly correlated multi-reference configuration interaction) were employed to compute the geometries and relative electronic energies for the X̃(1)A(') and Ã(1)A(″) states of HAsO. These are the highest level calculations on these states yet reported. The MRCI-F12 method gives computed T0 (adiabatic transition energy including zero-point energy correction) values, which agree well with the available experimental T0 value much better than previously computed values and values computed with other MR methods in this work. In addition, the potential energy surfaces of the X̃(1)A(') and Ã(1)A(″) states of HAsO were computed using the MRCI-F12 method. Franck-Condon factors between the two states, which include anharmonicity and Duschinsky rotation, were then computed and used to simulate the recently reported SVL emission spectra of HAsO and DAsO [R. Grimminger and D. J. Clouthier, J. Chem. Phys. 135, 184308 (2011)]. Our simulated SVL emission spectra confirm the assignments of the molecular carrier, the electronic states involved, and the vibrational structures observed in the SVL emission spectra but suggest a loss of intensity in the reported experimental spectra at the low emission energy region almost certainly due to a loss of responsivity near the cutoff region (∼800 nm) of the detector used. Computed and experimentally derived re (equilibrium) and/or r0 {the (0,0,0) vibrational level} geometries of the two states of HAsO are discussed.

Comparison of methods for calculating Franck–Condon factors beyond the harmonic approximation: how important are Duschinsky rotations?

Three different approaches for calculating Franck–Condon factors beyond the harmonic approximation are compared and discussed in detail. Duschinsky effects are accounted for either by a rotation of the initial or final wavefunctions – which are obtained from state-specific configuration-selective vibrational configuration interaction calculations – or by a rotation of the underlying multi-dimensional potential energy surfaces being determined from explicitly correlated coupled-cluster approaches. An analysis of the Duschinsky effects in dependence on the rotational angles and the anisotropy of the wavefunction is provided. Benchmark calculations for the photoelectron spectra of ClO2, HS−2 and ZnOH− are presented. An application of the favoured approach for calculating Franck–Condon factors to the oxidation of Zn(H2O)+ and Zn2(H2O)+ demonstrates its applicability to systems with more than three atoms.

Quantum dynamics of radiationless electronic transitions including normal modes displacements and Duschinsky rotations: a second-order cumulant approach.

An analytical expression for the population dynamics of electronic radiationless transitions has been derived from the second order expansion of the quantum evolution operator in the Liouville space and the cumulant theory. The expression includes the effect of both normal mode displacements and Duschinsky rotations and allows to take into account both equilibrium and nonequilibrium initial conditions. The methodology has been applied to model the electron-transfer process between the accessory bacteriochlorophyll and the bacteriopheophytine in bacterial reactions centers, providing a rate in good agreement with experimental findings.

The effect of Duschinsky rotation on charge transport properties of molecular junctions in the sequential tunneling regime.

We present here a systematic theoretical study on the effect of Duschinsky rotation on charge transport properties of molecular junctions in the sequential tunneling regime. In the simulations we assume that only two electronic charging states each coupled to a two dimensional vibrational potential energy surface (PES) are involved in the transport process. The Duschinsky rotation effect is accounted by varying the rotational angle between the two sets of displaced PESs. Both harmonic potential and anharmonic Morse potential have been considered for the cases of the intermediate to strong electron-vibration couplings. Our calculations show that the inclusion of the Duschinsky rotation effect can significantly change the charge transport properties of a molecular junction. Such an effect makes the otherwise symmetric Coulomb diamond become asymmetric in harmonic potentials. Depending on the angle of the rotation, the low bias current could be significantly suppressed or enhanced. This effect is particularly prominent in the Franck-Condon (FC) blockade regime where the electron-vibration coupling is strong. These changes are caused by the variation of the FC factors which are closely related to the rotational angle between the two sets of PESs involved in the charge transport process. For a molecular junction with Morse potentials, the changes caused by Duschinsky rotation are much more complicated. Both the amplitude and shape of the Coulomb diamond are closely dependent on the rotational angle in the whole range from 0 to 2π. One interesting result is that with a rotation angle of π (and also π/2 for certain cases) symmetric Coulomb diamonds can even be formed from the intrinsically asymmetric Morse potential. These results could be important for the interpretation of experimental observations.

Theoretical Study of the Phosphorescence Spectrum of Tris(2-phenylpyridine)iridium Using the Displaced Harmonic Oscillator Model

We present a comprehensive investigation of the phosphorescence spectrum of Ir(ppy)3 (ppy=2-phenylpyridine), which is greatly influenced by vibration of the complex. General formalism of the emission spectrum is derived using a thermal vibration correlation function formalism for the transition between two adiabatic electronic states in polyatomic molecules. Displacements and Duschinsky rotation of potential energy surfaces are included within the framework of a multidimensional harmonic oscillator model. This formalism gives a reliable description of the emission spectrum of Ir(ppy)3. The calculated results indicated that the 0→1 transition between the T1 state and the S0 state makes a large contribution to the emission spectrum, especially the vibrational modes below 1600 cm–1. The breathing vibration of the ligands and the CC and CN stretching vibrations of benzene and pyridine rings are the main reasons for the appearance of the shoulder peak in the spectrum. The Boltzmann distribution makes the intensities of both the main and the shoulder peaks decrease, and the peaks are close together. When coupled with first-principles density functional theory (DFT) calculations, the present approach appears to be an effective tool to obtain a quantitative description and detailed understanding of the spectra and photophysical processes of polyatomic molecules.

Aggregation effects on the optical emission of 1,1,2,3,4,5-hexaphenylsilole (HPS): a QM/MM study.

We investigate the photophysical property for 1,1,2,3,4,5-hexaphenylsilole (HPS) through combined quantum mechanical and molecular mechanical (QM/MM) simulations. Under the displaced harmonic oscillator approximation with consideration of the Duschinsky rotation effect (DRE), the radiative and nonradiative rates of the excited-state decay processes for HPS are calculated by using the analytical vibration correlation function approach coupled with first-principles calculations. The intermolecular packing effect is incorporated through electrostatic interaction modeled by a force field. We find that from the gas phase to the solid state (i) the side phenyl ring at the 5-position becomes coplanar with the central silacycle, which increases the degree of conjugation, thus accelerating the radiative decay process, and (ii) the rotation of the side phenyl ring at the 2-position is restricted, which blocks the excited-state nonradiative decay channels. Such a synergetic effect largely enhances the solid-state luminescence quantum efficiency through reducing the nonradiative decay rate by about 4 orders of magnitude, leading to the radiative decay overwhelming the nonradiatvie decay. In addition, the calculated solid-phase absorption and emission optical spectra of HPS are found to be in agreement with the experiment.

Simulation of the single-vibronic-level emission spectrum of HPS.

We have computed the potential energy surfaces of the X¹A' and ùA" states of HPS using the explicitly correlated multi-reference configuration interaction (MRCI-F12) method, and Franck-Condon factors between the two states, which include anharmonicity and Duschinsky rotation, with the aim of testing the assignment of the recently reported single-vibronic-level (SVL) emission spectrum of HPS [R. Grimminger, D. J. Clouthier, R. Tarroni, Z. Wang, and T. J. Sears, J. Chem. Phys. 139, 174306 (2013)]. These are the highest level calculations on these states yet reported. It is concluded that our spectral simulation supports the assignments of the molecular carrier, the electronic states involved and the vibrational structure of the experimental laser induced fluorescence, and SVL emission spectra proposed by Grimminger et al. [J. Chem. Phys. 139, 174306 (2013)]. However, there remain questions unanswered regarding the relative electronic energies of the two states and the geometry of the excited state of HPS.

Analysis of the Photoelectron Spectra of Selenium Difluoride and Selenium Dichloride Based on Franck-Condon Factors

ABSTRACT The vibrational structure of the photoelectron spectra of selenium difluoride and selenium dichloride have been simulated using the computed Franck-Condon factors in the harmonic oscillator approximation. Spectral simulations have been carried out employing the coupled-cluster singles, doubles, and triples (CCSD(T)) and the Becke three-parameter Lee, Yang, and Parr (B3LYP) values for the ground electronic states of the neutral molecules and the cations selenium difluoride and selenium dichloride, respectively. The Duschinsky rotations among the normal modes of two ground electronic states of species involved in the transition are fully taken into account. The ionization energies obtained for selenium difluoride and selenium dichloride are in reasonable agreement with the experimentally determined values. The spectral simulations of vibrational structures including frequency changes and Duschinsky rotation upon the electronic excitation are in agreement with the experimental results.