Density functional calculations of the vibronic structure of electronic absorption spectra

Dierksen, Marc; Grimme, Stefan

doi:10.1063/1.1642595

Cited by 308 publications

(309 citation statements)

References 83 publications

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“…[33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48] Adding a further dimension to efforts along those lines and of relevance for determining which type of transition (vertical or adiabatic) best corresponds to experimental absorption maxima, are simulations of vibrationally resolved electronic absorption spectra reported by a number of research groups. [49][50][51][52][53] Such simulations require computation of vibrational wavefunctions and their overlap (Franck-Condon factors), and may also include a dependence of the electronic dipole moment operator on nuclear coordinates (Herzberg-Teller corrections).…”

Section: Introductionmentioning

confidence: 99%

How Method-Dependent Are Calculated Differences between Vertical, Adiabatic, and 0–0 Excitation Energies?

2014

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ABSTRACT:Through a large number of benchmark studies, the performance of different quantum chemical methods in calculating vertical excitation energies is today quite well established. Furthermore, these efforts have in recent years been complemented by a few benchmarks focusing instead on adiabatic excitation energies. However, it is much less well established how calculated differences between vertical, adiabatic and 0-0 excitation energies vary between methods, which may be due to the cost of evaluating zero-point vibrational energy corrections for excited states. To fill this gap, we have calculated vertical, adiabatic and 0-0 excitation energies for a benchmark set of molecules covering both organic and inorganic systems. Considering in total 96 excited states and using both TD-DFT with a variety of exchange-correlation functionals and the ab initio CIS and CC2 methods, it is found that while the vertical excitation energies obtained with the various methods show an average (over the 96 states) standard deviation of 0.39 eV, the corresponding standard deviations for the differences between vertical, adiabatic and 0-0 excitation energies are much smaller: 0.10 (difference between adiabatic and vertical) and 0.02 eV (difference between 0-0 and adiabatic). These results provide a quantitative measure showing that the calculation of such quantities in photochemical modeling is well amenable to low-level methods. In addition, we also report on how these energy differences vary between chemical systems and assess the performance of TD-DFT, CIS and CC2 in reproducing experimental 0-0 excitation energies.

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Section: Introductionmentioning

confidence: 99%

How Method-Dependent Are Calculated Differences between Vertical, Adiabatic, and 0–0 Excitation Energies?

2014

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“…It has recently been applied successfully in combination with TDDFT excited-state optimizations to model the absorption spectra of organic compounds by Dierksen and Grimme. 21,22 As has been mentioned in ref 23, however, the Franck-Condon approach might have problems in some cases if (i) the excited-state minimum is largely displaced from the ground-state minimum, (ii) there are (near-) degenerate excited states that result in a complicated topology of the potential energy surfaces (PESs), or (iii) no excited-state minimum due to, for example, conical intersections can be found.…”

Section: Introductionmentioning

confidence: 99%

Vibronic Structure of the Permanganate Absorption Spectrum from Time-Dependent Density Functional Calculations

2005

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The UV absorption spectrum of the permanganate anion is a prototype transition-metal complex spectrum. Despite this being a simple d 0 T d system, for which a beautiful spectrum with detailed vibrational structure has been available since 1967, the assignment of the second and third bands is still very controversial. The issue can be resolved only by an elucidation of the intricate vibronic structure of the spectrum. We investigate the vibronic coupling by means of linear-response time-dependent density functional calculations. By means of a diabatizing scheme that employs the transition densities obtained in the TDDFT calculations in many geometries around R e , we construct a Taylor series expansion in the normal coordinates of a diabatic potential energy matrix, coupling 24 excited states. The simulated vibronic structure is in good agreement with the experimental absorption spectrum after the adjustment of some of the calculated vertical excitation energies. The peculiar blurred vibronic structure of the second band, which is a very distinctive feature of the experimental spectrum, is fully reproduced in the calculations. It is caused by the double-well shape of the adiabatic energy surface along the Jahn-Teller active e mode of the allowed 1 E state arising from the second 1 T 2 state, which exhibits a Jahn-Teller splitting into 1 B 2 and 1 E states. We trace the double-well shape to an avoided crossing between two diabatic states with different orbital-excitation character. The crossing can be explained at the molecular orbital level from the Jahn-Teller splitting of the set of 7t 2 {3d xy , 3d xz , 3d yz } orbitals (the LUMO + 1), to which the excitations characterizing the diabatic states take place. In contrast to its character in the two well regions, at R e the 2 1 T 2 state is not predominantly an excitation to the LUMO + 1, but has more HOMO -1 f LUMO (2e ) {3d x 2 -y 2 , 3d z 2 }) character. The changing character of the 2 1 T 2 -1 E state along the e mode implies that the assignment of the experimental bands to single orbital transitions is too simplistic intrinsically. This spectrum, and notably the blurring of the vibronic structure in the second band, can be understood only from the extensive configurational mixing and vibronic coupling between the excited states. This solves the long-standing assignment problem of these bands.

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“…A direct comparison of the simulations in acetonitrile and water, however, indicates a shift of 0.11 eV between these two solvents, compared with an experimental shift of <0.01 eV. 18 Moreover, it is known from CPMD simulations 10 or studies of the vibrational broadening of absorption bands [25][26][27] that vertical excitation energies and band maxima for gas-phase molecules often differ by 0.1-0.2 eV; so, this aspect should be taken into account in the calculation of shifts in excitation energies. Hence, in the present study, we want to assess the quality of the frozen-density embedding scheme in combination with a classical MD simulation for the calculation of solvatochromic shifts.…”

Section: Introductionmentioning

confidence: 99%

An Explicit Quantum Chemical Method for Modeling Large Solvation Shells Applied to Aminocoumarin C151

et al. 2005

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The absorption spectra of aminocoumarin C151 in water and n-hexane solution are investigated by an explicit quantum chemical solvent model. We improved the efficiency of the frozen-density embedding scheme, as used in a former study on solvatochromism (J. Chem. Phys. 2005, 122, 094115) to describe very large solvent shells. The computer time used in this new implementation scales approximately linearly (with a low prefactor) with the number of solvent molecules. We test the ability of the frozen-density embedding to describe specific solvent effects due to hydrogen bonding for a small example system, as well as the convergence of the excitation energy with the number of solvent molecules considered in the solvation shell. Calculations with up to 500 water molecules (1500 atoms) in the solvent system are carried out. The absorption spectra are studied for C151 in aqueous or n-hexane solution for direct comparison with experimental data. To obtain snapshots of the dye molecule in solution, for which subsequent excitation energies are calculated, we use a classical molecular dynamics (MD) simulation with a force field adapted to first-principles calculations. In the calculation of solvatochromic shifts between solvents of different polarity, the vertical excitation energy obtained at the equilibrium structure of the isolated chromophore is sometimes taken as a guess for the excitation energy in a nonpolar solvent. Our results show that this is, in general, not an appropriate assumption. This is mainly due to the fact that the solute dynamics is neglected. The experimental shift between n-hexane and water as solvents is qualitatively reproduced, even by the simplest embedding approximation, and the results can be improved by a partial polarization of the frozen density. It is shown that the shift is mainly due to the electronic effect of the water molecules, and the structural effects are similar in n-hexane and water. By including water molecules, which might be directly involved in the excitation, in the embedded region, an agreement with experimental values within 0.05 eV is achieved.

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Density functional calculations of the vibronic structure of electronic absorption spectra

Cited by 308 publications

References 83 publications

How Method-Dependent Are Calculated Differences between Vertical, Adiabatic, and 0–0 Excitation Energies?

How Method-Dependent Are Calculated Differences between Vertical, Adiabatic, and 0–0 Excitation Energies?

Vibronic Structure of the Permanganate Absorption Spectrum from Time-Dependent Density Functional Calculations

An Explicit Quantum Chemical Method for Modeling Large Solvation Shells Applied to Aminocoumarin C151

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