Magnus W. D. Hanson-Heine

Investigating the calculation of anharmonic vibrational frequencies using force fields derived from density functional theory.

The calculation of anharmonic vibrational frequencies for a set of small molecules has been examined to explore the merit of applying such computationally expensive approaches for large molecules with density functional theory. The performance of different hybrid and gradient-corrected exchange-correlation functionals has been assessed for the calculation of anharmonic vibrational frequencies using second-order vibrational perturbation theory with two- and four-mode couplings and compared to the recently developed transition optimized shifted Hermite method. A range of exchange-correlation functionals (B3LYP, BLYP, EDF1, EDF2, B97-1, B97-2, HCTH-93, HCTH-120, HCTH-147, and HCTH-407) have been evaluated with reference to a large experimental data set comprising 88 species and 655 modes as well as a smaller set of shifts in frequency because of anharmonicity derived from experimental data. The anharmonic frequencies calculated using hybrid functionals provide the best agreement with experiment, and are not significantly improved by frequency scaling factors, indicating an absence of significant systematic error. For the molecules studied, the B97-1 and B97-2 functionals give the closest overall agreement with experiment, although the improvement over the best case for pure harmonic frequencies is modest. Predictions of the experimental anharmonic shifts are closest for the B3LYP and EDF2 functionals, with B97-1 performing well because of a good description of the harmonic force field. Investigations using modified hybrid functionals with increased fractions of Hartree-Fock exchange indicate that approximately 20% Hartree-Fock exchange is optimal.

Calculating excited state properties using Kohn-Sham density functional theory.

The accuracy of excited states calculated with Kohn-Sham density functional theory using the maximum overlap method has been assessed for the calculation of adiabatic excitation energies, excited state structures, and excited state harmonic and anharmonic vibrational frequencies for open-shell singlet excited states. The computed Kohn-Sham adiabatic excitation energies are improved significantly by post self-consistent field spin-purification, but remain too low compared with experiment with a larger error than time-dependent density functional theory. Excited state structures and vibrational frequencies are also improved by spin-purification. The structures show a comparable accuracy to time-dependent density functional theory, while the harmonic vibrational frequencies are found to be more accurate for the majority of vibrational modes. The computed harmonic vibrational frequencies are also further improved by perturbative anharmonic corrections, suggesting a good description of the potential energy surface. Overall, excited state Kohn-Sham density functional theory is shown to provide an efficient method for the calculation of excited state structures and vibrational frequencies in open-shell singlet systems and provides a promising technique that can be applied to study large systems.

Photochemical Dihydrogen Production Using an Analogue of the Active Site of [NiFe] Hydrogenase

Photoproduction of dihydrogen (H2) by a low molecular weight analogue of the active site of [NiFe] hydrogenase has been investigated by reduction of the [NiFe2] cluster, 1, by a photosensitier PS (PS = [ReCl(CO)3(bpy)] or [Ru(bpy)3][PF6]2). Reductive quenching of the (3)MLCT excited state of the photosensitizer by NEt3 or N(CH2CH2OH)3 (TEOA) generates PS(•-), and subsequent intermolecular electron transfer to 1 produces the reduced anionic form of 1. Time-resolved infrared spectroscopy (TRIR) has been used to probe the intermediates throughout the reduction of 1 and subsequent photocatalytic H2 production from [HTEOA][BF4], which was monitored by gas chromatography. Two structural isomers of the reduced form of 1 (1a(•-) and 1b(•-)) were detected by Fourier transform infrared spectroscopy (FTIR) in both CH3CN and DMF (dimethylformamide), while only 1a(•-) was detected in CH2Cl2. Structures for these intermediates are proposed from the results of density functional theory calculations and FTIR spectroscopy. 1a(•-) is assigned to a similar structure to 1 with six terminal carbonyl ligands, while calculations suggest that in 1b(•-) two of the carbonyl groups bridge the Fe centers, consistent with the peak observed at 1714 cm(-1) in the FTIR spectrum for 1b(•-) in CH3CN, assigned to a ν(CO) stretching vibration. Formation of 1a(•-) and 1b(•-) and production of H2 was studied in CH3CN, DMF, and CH2Cl2. Although the more catalytically active species (1a(•-) or 1b(•-)) could not be determined, photocatalysis was observed only in CH3CN and DMF.

Photoaquation Mechanism of Hexacyanoferrate(II) ions: Ultrafast 2D UV and Transient Visible and IR Spectroscopies.

Ferrous iron(II) hexacyanide in aqueous solutions is known to undergo photoionization and photoaquation reactions depending on the excitation wavelength. To investigate this wavelength dependence, we implemented ultrafast two-dimensional UV transient absorption spectroscopy, covering a range from 280 to 370 nm in both excitation and probing, along with UV pump/visible probe or time-resolved infrared (TRIR) transient absorption spectroscopy and density functional theory (DFT) calculations. As far as photoaquation is concerned, we find that excitation of the molecule leads to ultrafast intramolecular relaxation to the lowest triplet state of the [Fe(CN)6]4- complex, followed by its dissociation into CN- and [Fe(CN)5]3- fragments and partial geminate recombination, all within <0.5 ps. The subsequent time evolution is associated with the [Fe(CN)5]3- fragment going from a triplet square pyramidal geometry, to the lowest triplet trigonal bipyramidal state in 3-4 ps. This is the precursor to aquation, which occurs in ∼20 ps in H2O and D2O solutions, forming the [Fe(CN)5(H2O/D2O)]3- species, although some aquation also occurs during the 3-4 ps time scale. The aquated complex is observed to be stable up to the microsecond time scale. For excitation below 310 nm, the dominant channel is photooxidation with a minor aquation channel. The photoaquation reaction shows no excitation wavelength dependence up to 310 nm, that is, it reflects a Kasha Rule behavior. In contrast, the photooxidation yield increases with decreasing excitation wavelength. The various intermediates that appear in the TRIR experiments are identified with the help of DFT calculations. These results provide a clear example of the energy dependence of various reactive pathways and of the role of spin-states in the reactivity of metal complexes.

Rapid anharmonic vibrational corrections derived from partial Hessian analysis.

Vibrational analysis within a partial Hessian framework can successfully describe the vibrational properties of a variety of systems where the vibrational modes of interest are localized within a specific region of the system. We have developed a new approach to calculating anharmonic frequencies based on vibrational frequencies and normal modes obtained from a partial Hessian analysis using second-order vibrational perturbation theory and the transition optimized shifted Hermite method. This allows anharmonic frequencies for vibrational modes that are spatially localized to be determined at a significantly reduced computational cost. Several molecular systems are examined in order to demonstrate the effectiveness of this method including organic molecules adsorbed on the Si(100)-2×1 surface, model peptides in solution, and the C-H stretching region of polycyclic aromatic hydrocarbons. Overall, for a range of systems, anharmonic frequencies calculated using the partial Hessian approach are found to be in close agreement with the results obtained using full anharmonic calculations while providing a significant reduction in computational cost.

Examining the impact of harmonic correlation on vibrational frequencies calculated in localized coordinates

Carefully choosing a set of optimized coordinates for performing vibrational frequency calculations can significantly reduce the anharmonic correlation energy from the self-consistent field treatment of molecular vibrations. However, moving away from normal coordinates also introduces an additional source of correlation energy arising from mode-coupling at the harmonic level. The impact of this new component of the vibrational energy is examined for a range of molecules, and a method is proposed for correcting the resulting self-consistent field frequencies by adding the full coupling energy from connected pairs of harmonic and pseudoharmonic modes, termed vibrational self-consistent field (harmonic correlation). This approach is found to lift the vibrational degeneracies arising from coordinate optimization and provides better agreement with experimental and benchmark frequencies than uncorrected vibrational self-consistent field theory without relying on traditional correlated methods.

Intermediate vibrational coordinate localization with harmonic coupling constraints

Optimized normal coordinates can significantly improve the speed and accuracy of vibrational frequency calculations. However, over-localization can occur when using unconstrained spatial localization techniques. The unintuitive mixtures of stretching and bending coordinates that result can make interpreting spectra more difficult and also cause artificial increases in mode-coupling during anharmonic calculations. Combining spatial localization with a constraint on the coupling between modes can be used to generate coordinates with properties in-between the normal and fully localized schemes. These modes preserve the diagonal nature of the mass-weighted Hessian matrix to within a specified tolerance and are found to prevent contamination between the stretching and bending vibrations of the molecules studied without a priori classification of the different types of vibration present. Relaxing the constraint can also be used to identify which normal modes form specific groups of localized modes. The new coordinates are found to center on more spatially delocalized functional groups than their fully localized counterparts and can be used to tune the degree of vibrational correlation energy during anharmonic calculations.

Simulation of Two-Dimensional Infrared Spectroscopy of Peptides Using Localized Normal Modes

Nonlinear two-dimensional infrared spectroscopy (2DIR) is most commonly simulated within the framework of the exciton method. The key parameters for these calculations include the frequency of the oscillators within their molecular environments and coupling constants that describe the strength of coupling between the oscillators. It is shown that these quantities can be obtained directly from harmonic frequency calculations by exploiting a procedure that localizes the normal modes. This approach is demonstrated using the amide I modes of polypeptides. For linear and cyclic diamides and hexapeptide Z-Aib-L-Leu-(Aib)2-Gly-Aib-OtBu, the computed parameters are compared with those from existing schemes, and the resulting 2DIR spectra are consistent with experimental observations. The incorporation of conformational averaging of structures from molecular dynamics simulations is discussed, and a hybrid scheme wherein the Hamiltonian matrix from the quantum chemical local-mode approach is combined with fluctuations from empirical schemes is shown to be consistent with experiment. The work demonstrates that localized vibrational modes can provide a foundation for the calculation of 2DIR spectra that does not rely on extensive parametrization and can be applied to a wide range of systems. For systems that are too large for quantum chemical harmonic frequency calculations, the local-mode approach provides a convenient platform for the development of site frequency and coupling maps.

Calculating singlet excited states: Comparison with fast time-resolved infrared spectroscopy of coumarins

In contrast to the ground state, the calculation of the infrared (IR) spectroscopy of molecular singlet excited states represents a substantial challenge. Here, we use the structural IR fingerprint of the singlet excited states of a range of coumarin dyes to assess the accuracy of density functional theory based methods for the calculation of excited state IR spectroscopy. It is shown that excited state Kohn-Sham density functional theory provides a high level of accuracy and represents an alternative approach to time-dependent density functional theory for simulating the IR spectroscopy of singlet excited states.

Kohn-Sham density functional theory calculations of non-resonant and resonant x-ray emission spectroscopy

The accuracy of non-resonant and resonant (resonant inelastic X-ray scattering) X-ray emission spectra simulated based upon Kohn-Sham density functional theory is assessed. Accurate non-resonant X-ray emission spectra with the correct energy scale are obtained when short-range corrected exchange-correlation functionals designed for the calculation of X-ray absorption spectroscopy are used. It is shown that this approach can be extended to simulate resonant inelastic X-ray scattering by using a reference determinant that describes a core-excited state. For this spectroscopy, it is found that a standard hybrid functional, B3LYP, gives accurate spectra that reproduce the features observed in experiment. However, the ability to correctly describe subtle changes in the spectra arising from different intermediate states is more challenging and requires averaging over conformations from a molecular dynamics simulation. Overall, it is demonstrated that accurate non-resonant and resonant X ray emission spectra can be simulated directly from Kohn-Sham density functional theory.