Franck-Condon factors based on anharmonic vibrational wave functions of polyatomic molecules

One- and two-photon absorption spectra of organoboron complexes: vibronic and environmental effects

We synthesized a series of four parent aza-β-ketoiminate organoboron complexes and performed spectroscopic studies using both experimental and computational techniques. We studied how benzannulation influences the vibronic structure of the UV/Vis absorption bands with a focus on the bright lowest-energy π → π* electronic excitation. Theoretical simulations, accounting for inhomogeneous broadening effects using different embedding schemes, allowed gaining in-depth insights into the observed differences in band shapes induced by structural modifications. We observed huge variations in the distributions of vibronic transitions depending on the position of benzannulation. By and large, the harmonic approximation combined with the adiabatic hessian model delivers qualitatively correct band shapes for the one-photon absorption spectra, except in one case. We also assessed the importance of non-Condon effects (accounted for by the linear term in Herzberg-Teller expansion of the dipole moment) for S0 → S1 band shapes. It turned out that non-Condon contributions have no effect on the band shape in one-photon absorption spectra. In contrast, these effects significantly change the Franck-Condon band shapes of the two-photon absorption spectra. For one of the studied organoboron complexes we also performed a preliminary exploration of mechanical anharmonicity, resulting in an increase of the intensity of the 0-0 transition, which improves the agreement with the experimental data compared to the harmonic model.

Reassignment of the Photoelectron Spectrum of Methylketene Using a Hybrid Model of Harmonic and Anharmonic Oscillators to Compute Franck-Condon Factors

We constructed a hybrid model of harmonic and anharmonic oscillators to compute Franck-Condon factors and interpret the photoelectron spectrum of methylketene. The equilibrium structures of methylketene and its cation were optimized, and then, the harmonic and anharmonic vibrational frequencies were computed using the B3LYP, PBE0, APFD, and ωB97XD approaches of the density functional theory. The photoelectron spectrum of methylketene was simulated by computing the Franck-Condon factors with both the harmonic and hybrid models. The adiabatic ionization energy of methylketene was computed by using the CCSD(T) approach extrapolating to the complete basis set limit. The simulated photoelectron spectra are consistent with those from the experiment for both the harmonic and hybrid models. However, the error in band positions is reduced by using the hybrid model. The computed adiabatic ionization energies of methylketene are in agreement with the experiment, with the smallest error being 0.017 eV. Our interpretation based on the theoretical spectrum led to the reassignment of the experimental photoelectron spectrum of methylketene.

Tailored anharmonic-harmonic vibrational profiles for fluorescent biomarkers

We propose a hybrid anharmonic-harmonic scheme for vibrational broadenings, which embeds a reduced-space vibrational configuration interaction (VCI) anharmonic wave function treatment in the independent-mode displaced harmonic oscillator (IMDHO) model. The resulting systematically-improvable VCI-in-IMDHO model allows including the vibronic effects of all vibrational degrees of freedom, while focusing the effort on the important degrees of freedom with minimal extra computational effort compared to a reduced-space VCI treatment. We show for oligothiophene examples that the VCI-in-IMDHO approach can yield accurate vibrational profiles employing smaller vibrational spaces in the VCI part than the reduced-space VCI approach. By this, the VCI-in-IMDHO model enables accurate calculation of vibrational profiles of common fluorescent dyes with more than 100 vibrational degrees of freedom. We illustrate this for three examples of fluorescent biomarkers of current interest. These are the oligothiophene-based fluorescent dye called HS84, 1,4-diphenylbutadiene, and an anthracene diimide. For all examples, we assess the impact of the anharmonic treatment on the vibrational broadening, which we find to be more pronounced for the intensities than for the peak positions.

Full-dimensional theoretical description of vibrationally resolved valence-shell photoionization of H2O

We have performed a full-dimensional theoretical study of vibrationally resolved photoelectron emission from the valence shell of the water molecule by using an extension of the static-exchange density functional theory that accounts for ionization as well as for vibrational motion in the symmetric stretching, antisymmetric stretching, and bending modes. At variance with previous studies performed in centrosymmetric molecules, where vibrationally resolved spectra are mostly dominated by the symmetric stretching mode, in the present case, all three modes contribute to the calculated spectra, including intermode couplings. We have found that diffraction of the ejected electron by the various atomic centers is barely visible in the ratios between vibrationally resolved photoelectron spectra corresponding to different vibrational states of the remaining H2O+ cation (the so-called v-ratios), in contrast to the prominent oscillations observed in K-shell ionization of centrosymmetric molecules, including those that only contain hydrogen atoms around the central atoms, e.g., CH4. To validate the conclusions of our work, we have carried out synchrotron radiation experiments at the SOLEIL synchrotron and determined photoelectron spectra and v-ratios for H2O in a wide range of photon energies, from threshold up to 150 eV. The agreement with the theoretical predictions is good.

Vibrationally resolved emission spectra of luminescent conjugated oligothiophenes from anharmonic calculations

We report on accurate and efficient calculations of vibrationally resolved emission spectra for oligothiophenes from anharmonic vibrational configuration interaction wave-function calculations in reduced vibrational spaces. These reduced spaces are chosen based on the independent mode displaced harmonic oscillator model. Good agreement with experiment is obtained for all-trans oligothiophenes with two to five rings also when employing only a few active modes. Vibrational modes incorporating inter-ring carbon-carbon stretches and a ring breathing mode are found to be the main players in the vibrational progression for the emission from the first excited electronic state for all investigated oligothiophene derivatives. The presented framework is here illustrated for oligothiophenes, but we have made no underlying system-dependent assumptions and believe it to become a valuable tool for the rational design of fluorescence biomarkers.

Understanding the interplay between the solvent and nuclear rearrangements in the negative solvatochromism of a push–pull flexible quinolinium cation

The main effects (solvation, vibronic progression) affecting the band position and shape of a push–pull flexible quinolinium cation OPA are highlighted.

General formulation of vibronic spectroscopy in internal coordinates

Our general platform integrating time-independent and time-dependent evaluations of vibronic effects at the harmonic level for different kinds of absorption and emission one-photon, conventional and chiral spectroscopies has been extended to support various sets of internal coordinates. Thanks to the implementation of analytical first and second derivatives of different internal coordinates with respect to cartesian ones, both vertical and adiabatic models are available, with the inclusion of mode mixing and, possibly, Herzberg-Teller contributions. Furthermore, all supported non-redundant sets of coordinates are built from a fully automatized algorithm using only a primitive redundant set derived from a bond order-based molecular topology. Together with conventional stretching, bending, and torsion coordinates, the availability of additional coordinates (including linear and out-of-plane bendings) allows a proper treatment of specific systems, including, for instance, inter-molecular hydrogen bridges. A number of case studies are analysed, showing that cartesian and internal coordinates are nearly equivalent for semi-rigid systems not experiencing significant geometry distortions between initial and final electronic states. At variance, delocalized (possibly weighted) internal coordinates become much more effective than their cartesian counterparts for flexible systems and/or in the presence of significant geometry distortions accompanying electronic transitions.

Performance of density functional theory in computing nonresonant vibrational (hyper)polarizabilities

A set of exchange-correlation functionals, including BLYP, PBE0, B3LYP, BHandHLYP, CAM-B3LYP, LC-BLYP, and HSE, has been used to determine static and dynamic nonresonant (nuclear relaxation) vibrational (hyper)polarizabilities for a series of all-trans polymethineimine (PMI) oligomers containing up to eight monomer units. These functionals are assessed against reference values obtained using the Møller-Plesset second-order perturbation theory (MP2) and CCSD methods. For the smallest oligomer, CCSD(T) calculations confirm the choice of MP2 and CCSD as appropriate for assessing the density functionals. By and large, CAM-B3LYP is the most successful, because it is best for the nuclear relaxation contribution to the static linear polarizability, intensity-dependent refractive index second hyperpolarizability, static second hyperpolarizability, and is close to the best for the electro-optical Pockels effect first hyperpolarizability. However, none of the functionals perform satisfactorily for all the vibrational (hyper)polarizabilities studied. In fact, in the case of electric field-induced second harmonic generation all of them, as well as the Hartree-Fock approximation, yield the wrong sign. We have also found that the Pople 6-31+G(d) basis set is unreliable for computing nuclear relaxation (hyper)polarizabilities of PMI oligomers due to the spurious prediction of a nonplanar equilibrium geometry.

Approximate solution of the mode-mode coupling integral: Application to cytosine and its deuterated derivative

Ab initio Hartree-Fock (HF), density functional theory (DFT) and second-order Møller-Plesset (MP2) methods were used to perform harmonic and anharmonic calculations for the biomolecule cytosine and its deuterated derivative. The anharmonic vibrational spectra were computed using the vibrational self-consistent field (VSCF) and correlation-corrected vibrational self-consistent field (CC-VSCF) methods. Calculated anharmonic frequencies have been compared with the argon matrix spectra reported in literature. The results were analyzed with focus on the properties of anharmonic couplings between pair of modes. A simple and easy to use formula for calculation of mode-mode coupling magnitudes has been derived. The key element in present approach is the approximation that only interactions between pairs of normal modes have been taken into account, while interactions of triples or more are neglected. FTIR and Raman spectra of solid state cytosine have been recorded in the regions 400-4000 cm(-1) and 60-4000 cm(-1), respectively. Vibrational analysis and assignments are based on calculated potential energy distribution (PED) values.

Toward effective and reliable fluorescence energies in solution by a new state specific polarizable continuum model time dependent density functional theory approach

A state specific (SS) model for the inclusion of solvent effects in time dependent density functional theory (TD-DFT) computations of emission energies has been developed and coded in the framework of the so called polarizable continuum model (PCM). The new model allows for a rigorous and effective treatment of dynamical solvent effects in the computation of fluorescence and phosphorescence spectra in solution, and it can be used for studying different relaxation time regimes. SS and conventional linear response (LR) models have been compared by computing the emission energies for different benchmark systems (formaldehyde in water and three coumarin derivatives in ethanol). Special attention is given to the influence of dynamical solvation effects on LR geometry optimizations in solution. The results on formaldehyde point out the complementarity of LR and SS approaches and the advantages of the latter model especially for polar solvents and/or weak transitions. The computed emission energies for coumarin derivatives are very close to their experimental counterparts, pointing out the importance of a proper treatment of nonequilibrium solvent effects on both the excited and the ground state energies. The availability of SS-PCM/TD-DFT models for the study of absorption and emission processes allows for a consistent treatment of a number of different spectroscopic properties in solution.

Efficient configuration selection scheme for vibrational second-order perturbation theory

A fast algorithm of vibrational second-order Moller-Plesset perturbation theory is proposed, enabling a substantial reduction in the number of vibrational self-consistent-field (VSCF) configurations that need to be summed in the calculations. Important configurations are identified a priori by assuming that a reference VSCF wave function is approximated well by harmonic oscillator wave functions and that fifth- and higher-order anharmonicities are negligible. The proposed scheme has reduced the number of VSCF configurations by more than 100 times for formaldehyde, ethylene, and furazan with an error in computed frequencies being not more than a few cm(-1).

Fermi resonance in CO2: A combined electronic coupled-cluster and vibrational configuration-interaction prediction

The authors present a first-principles prediction of the energies of the eight lowest-lying anharmonic vibrational states of CO(2), including the fundamental symmetric stretching mode and the first overtone of the fundamental bending mode, which undergo a strong coupling known as Fermi resonance. They employ coupled-cluster singles, doubles, and (perturbative) triples [CCSD(T) and CCSDT] in conjunction with a range of Gaussian basis sets (up to cc-pV5Z, aug-cc-pVQZ, and aug-cc-pCVTZ) to calculate the potential energy surfaces (PESs) of the molecule, with the errors arising from the finite basis-set sizes eliminated by extrapolation. The resulting vibrational many-body problem is solved by the vibrational self-consistent-field and vibrational configuration-interaction (VCI) methods with the PESs represented by a fourth-order Taylor expansion or by numerical values on a Gauss-Hermite quadrature grid. With the VCI, the best theoretical estimates of the anharmonic energy levels agree excellently with experimental values within 3.5 cm(-1) (the mean absolute deviation). The theoretical (experimental) anharmonic frequencies of the Fermi doublet are 1288.9 (1285.4) and 1389.3 (1388.2) cm(-1).

Vibrational structure theory: new vibrational wave function methods for calculation of anharmonic vibrational energies and vibrational contributions to molecular properties

A number of recently developed theoretical methods for the calculation of vibrational energies and wave functions are reviewed. Methods for constructing the appropriate quantum mechanical Hamilton operator are briefly described before reviewing a particular branch of theoretical methods for solving the nuclear Schrödinger equation. The main focus is on wave function methods using the vibrational self-consistent field (VSCF) as starting point, and includes vibrational configuration interaction (VCI), vibrational Møller-Plesset (VMP) theory, and vibrational coupled cluster (VCC) theory. The convergence of the different methods towards the full vibrational configuration interaction (FVCI) result is discussed. Finally, newly developed vibrational response methods for calculation of vibrational contributions to properties, energies, and transition probabilities are discussed.

A variational approach for calculating Franck-Condon factors including mode-mode anharmonic coupling

We have implemented our new procedure for computing Franck-Condon factors utilizing vibrational configuration interaction based on a vibrational self-consistent field reference. Both Duschinsky rotations and anharmonic three-mode coupling are taken into account. Simulations of the first ionization band of ClO(2) and C(4)H(4)O (furan) using up to quadruple excitations in treating anharmonicity are reported and analyzed. A developer version of the MIDASCPP code was employed to obtain the required anharmonic vibrational integrals and transition frequencies.