Excited State Vibrational Frequencies Research Articles

Spectroscopic and Computational Observation of Glutamine Tautomerization in the Blue Light Sensing Using Flavin Domain Photoreaction.

Blue light sensing using flavin (BLUF) domains constitute a family of flavin-binding photoreceptors of bacteria and eukaryotic algae. BLUF photoactivation proceeds via a light-driven hydrogen-bond switch among flavin adenine dinucleotide (FAD) and glutamine and tyrosine side chains, whereby FAD undergoes electron and proton transfer with tyrosine and is subsequently re-oxidized by a hydrogen back-shuttle in picoseconds, constituting an important model system to understand proton-coupled electron transfer in biology. The specific structure of the hydrogen-bond patterns and the prevalence of glutamine tautomeric states in dark-adapted (DA) and light-activated (LA) states have remained controversial. Here, we present a combined femtosecond stimulated Raman spectroscopy (FSRS), computational chemistry, and site-selective isotope labeling Fourier-transform infrared spectroscopy (FTIR) study of the Slr1694 BLUF domain. FSRS showed distinct vibrational bands from the FADS1 singlet excited state. We observed small but significant shifts in the excited-state vibrational frequency patterns of the DA and LA states, indicating that these frequencies constitute a sensitive probe for the hydrogen-bond arrangement around FAD. Excited-state model calculations utilizing four different realizations of hydrogen bond patterns and glutamine tautomeric states were consistent with a BLUF reaction model that involved glutamine tautomerization to imidic acid, accompanied by a rotation of its side chain. A combined FTIR and double-isotope labeling study, with 13C labeling of FAD and 15N labeling of glutamine, identified the glutamine imidic acid C═N stretch vibration in the LA state and the Gln C═O in the DA state. Hence, our study provides support for glutamine tautomerization and side-chain rotation in the BLUF photoreaction.

Good Vibrations: Calculating Excited-State Frequencies Using Ground-State Self-Consistent Field Models.

The use of Δ-self-consistent field (SCF) approaches for studying excited electronic states has received a renewed interest in recent years. In this work, the use of this scheme for calculating excited-state vibrational frequencies is examined. Results from Δ-SCF calculations for a set of representative molecules are compared with those obtained using configuration interaction with single substitutions (CIS) and time-dependent density functional theory (TD-DFT) methods. The use of an approximate spin purification model is also considered for cases where the excited-state SCF solution is spin-contaminated. The results of this work demonstrate that an SCF-based description of an excited-state potential energy surface can be an accurate and cost-effective alternative to CIS and TD-DFT methods.

Calculation of vibrationally resolved absorption and fluorescence spectra of the rylenes.

A generating function method was used to simulate the vibrationally resolved absorption and emission spectra of perylene, terrylene and quaterrylene. This method operates on the basis of adiabatic excitation energies and electronic ground and excited state vibrational frequencies. These parameters were calculated using density functional theory with the PBE0 functional for perylene and terrylene and with the BH-LYP functional for quaterrylene. The vertical excitation energies of the lower excited states were calculated using functionals with differing amounts of Hartree-Fock exchange. The optimal functional for each molecule was chosen by comparing these energies to literature excitation energies. Using this technique the calculated absorption spectra and the calculated emission spectrum of perylene were found to be in excellent agreement with the literature experimental spectra after introducing a shift and a scaling factor. The most prominent bands of the absorption spectra were assigned to their respective vibronic transitions.

Electronically excited state geometries and vibrational frequencies calculated using the algebraic diagrammatic construction scheme for the polarization propagator

• The aug-cc-pVTZ basis set shows convergence for the properties and methods tested. • Geometries using ADC methods are similar in accuracy to TDDFT. • Harmonic frequencies are well treated by ADC methods and improve with the order. • Scaling factors can be used to improve ADC harmonic frequencies. • Spin-Opposite-Scaling further improves the frequency match for the ADC(2). The algebraic diagrammatic construction (ADC) scheme for the polarization propagator provides a series of ab initio methods for the calculation of electronically excited states. Here we examine the accuracy of these methods for calculating excited state geometries and excited state harmonic vibrational frequencies for open-shell singlet excited states. A range of ADC methods have been assessed up to third-order, including both the strict and extended second-order schemes and spin-opposite scaling. Third-order ADC is found to provide a high level of agreement for both the experimental excited state geometry and frequency values, while second-order ADC is improved using spin-opposite scaling.

Excited-State Vibrational Frequencies: Restricted Virtual Space Time-Dependent Density Functional Theory.

Calculating accurate vibrational frequencies for molecules with electronically excited states has an important function in many areas of photochemistry. However, calculations are often limited to smaller molecules due to the rapid growth in the degrees of freedom that must be taken into account to accurately describe larger systems. The applicability of the restricted virtual space (RVS) approximation has been studied within adiabatic linear response time-dependent density functional theory when calculating excited-state nuclear vibrational frequencies. Using the S1 and T1 electronic states of CO, CN-, HOF, H2CS, and C2H4 as representative examples, it is found that vibrational frequency calculations are particularly sensitive to this approximation, with no more than 10-20% of orbitals recommended for safe removal without a priori knowledge when using the 6-311+G(d,p) and aug-cc-pVTZ basis sets. Higher-frequency vibrations such as those with a high degree of CH bond stretching character are found to be less sensitive to the RVS than the lower-frequency vibrations, and several of the triplet states are also found to be less sensitive to this approximation than their equivalent singlet states. Occupied core orbitals and high-energy virtual orbitals with core character can also be removed without introducing significant error.

Anharmonic excited state frequencies of para-difluorobenzene, toluene and catechol using analytic RI-CC2 second derivatives.

Analytic second nuclear derivatives for excited electronic state energies have been implemented for the resolution-of-the-identity accelerated CC2, CIS(D∞) and ADC(2) models. Our efficient implementation with O(N2) memory demands enables the treatment of medium sized molecules with large basis sets and high numerical precision and thereby paves the way for semi-numerical evaluation of the higher-order derivatives required for anharmonic corrections to excited state vibrational frequencies. We compare CC2 harmonic and anharmonic excited state frequencies with experimental values for para-difluorobenzene, toluene and catechol. Basis set problems occur for out-of-plane bending vibrations due to intramolecular basis set superposition error. For non-planar molecules and in plane modes of planar molecules, the agreement between theory and experiment is better than 30 cm-1 on average and we reassign a number of experimental bands on the basis of the ab initio predictions.

Excitation energy transfer in phycobiliproteins of the cyanobacterium Acaryochloris marina investigated by spectral hole burning.

The cyanobacterium Acaryochloris marina developed two types of antenna complexes, which contain chlorophyll-d (Chl d) and phycocyanobilin (PCB) as light-harvesting pigment molecules, respectively. The latter membrane-extrinsic complexes are denoted as phycobiliproteins (PBPs). Spectral hole burning was employed to study excitation energy transfer and electron-phonon coupling in PBPs. The data reveal a rich spectral substructure with a total of four low-energy electronic states whose absorption bands peak at 633, 644, 654, and at about 673nm. The electronic states at ~633 and 644nm can be tentatively attributed to phycocyanin (PC) and allophycocyanin (APC), respectively. The remaining low-energy electronic states including the terminal emitter at 673nm may be associated with different isoforms of PC, APC, or the linker protein. Furthermore, the hole burning data reveal a large number of excited state vibrational frequencies, which are characteristic for the chromophore PCB. In summary, the results are in good agreement with the low-energy level structure of PBPs and electron-phonon coupling parameters reported by Gryliuk et al. (BBA 1837:1490-1499, 2014) based on difference fluorescence line-narrowing experiments.

Assessment of mode-mixing and Herzberg-Teller effects on two-photon absorption and resonance hyper-Raman spectra from a time-dependent approach

A time-dependent approach is presented to simulate the two-photon absorption (TPA) and resonance hyper-Raman scattering (RHRS) spectra including Duschinsky rotation (mode-mixing) and Herzberg-Teller (HT) vibronic coupling effects. The computational obstacles for the excited-state geometries, vibrational frequencies, and nuclear derivatives of transition dipole moments, which enter the expressions of TPA and RHRS cross sections, are further overcome by the recently developed analytical excited-state energy derivative approaches in the framework of time-dependent density functional theory. The excited-state potential curvatures are evaluated at different levels of approximation to inspect the effects of frequency differences, mode-mixing and HT on TPA and RHRS spectra. Two types of molecules, one with high symmetry (formaldehyde, p-difluorobenzene, and benzotrifluoride) and the other with non-centrosymmetry (cis-hydroxybenzylidene-2,3-dimethylimidazolinone in the deprotonated anion state (HDBI(-))), are used as test systems. The calculated results reveal that it is crucial to adopt the exact excited-state potential curvatures in the calculations of TPA and RHRS spectra even for the high-symmetric molecules, and that the vertical gradient approximation leads to a large deviation. Furthermore, it is found that the HT contribution is evident in the TPA and RHRS spectra of HDBI(-) although its one- and two-photon transitions are strongly allowed, and its effect results in an obvious blueshift of the TPA maximum with respect to the one-photon absorption maximum. With the HT and solvent effects getting involved, the simulated blueshift of 1291 cm(-1) agrees well with the experimental measurement.

Studies on the Way of Obtain Macroion C<sub>5</sub>H<sub>8</sub>O<sup>+</sup> by the Ring of C<sub>7</sub>H<sub>12</sub>O<sup>+</sup>

Using the CIS(Configuration Interaction with Single Substitute) method, we calculate the excited state structure and vibrational frequencies of cycloheptanone ion.

The Way of Obtain C<sub>3</sub>H<sub>4</sub>O<sup>+</sup> Fragments Laser-Induced by Cycloheptanone Ion<sup> </sup>Excited State

Our theoretical study aims to the way of obtain C3H4O+ fragments laser-induced by Cycloheptanone ion (C7H12O+ ) excited state and gives out a result with proved and directed significance for the corresponding experiments. Using the CIS（Configuration Interaction with Single Substitute） method, calculated Cycloheptanone ion excited state structure and vibrational frequencies.

The Way of Obtain C<sub>5</sub>H<sub>7</sub>O<sup>+ </sup>Fragments Laser-Induced by Cycloheptanone Ion Excited State

Our theoretical study aims to the way of obtain C5H7O+ fragments laser-induced by Cycloheptanone ion (C7H12O+) excited state and gives out a result with proved and directed significance for the corresponding experiments. Using the CIS（Configuration Interaction with Single Substitute） method, calculated cycloheptanone ion excited state structure and vibrational frequencies.

Analytical derivative techniques for TDDFT excited-state properties: Theory and application

We review our recent work on the methodology development of the excited-state properties for the molecules in vacuum and liquid solution. The general algorithms of analytical energy derivatives for the specific properties such as the first and second geometrical derivatives and IR/Raman intensities are demonstrated in the framework of the time-dependent density functional theory (TDDFT). The performance of the analytical approaches on the calculation of excited-state energy Hessian has also been shown. It is found that the analytical approaches are superior to the finite-difference method on the computational accuracy and efficiency. The computational cost for a TDDFT excited-state Hessian calculation is only 2–3 times as that for the DFT ground-state Hessian calculation. With the low computational complexity of the developed analytical approaches, it becomes feasible to realize the large-scale numerical calculations on the excited-state vibrational frequencies, vibrational spectroscopies and the electronic-structure parameters which enter the spectrum calculations of electronic absorption and emission, and resonance Raman spectroscopies for medium-to large-sized systems.

Normal modes and the Duschinsky mixing of the ground- and excited-state vibrations of the green fluorescent protein chromophore

Ground- and excited-state vibrational frequencies were calculated for the chromophore of the green fluorescent protein (GFP) using the complete active space self-consistent field (CASSCF) method and detailed normal-mode analyses were carried out for ground and excited states. The mixing of the vibrational modes between the different states was studied by applying the Duschinsky effect by the expressing excited-state normal modes in terms of the ground-state normal modes. It was found that the low-frequency vibrational modes in the vertical excited state play a significant role in structural adjustment.

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.

ZrFe, a Sextuply-Bonded Diatomic Transition Metal?

Diatomic ZrFe has been spectroscopically investigated for the first time, with the optical spectrum recorded in the range from 13890 cm(-1) to 18870 cm(-1). In the region from 13890 to 17500 cm(-1), a single exceptionally weak vibrational progression is found. Band origins, excited state vibrational frequencies and anharmonicities, excited state lifetimes, and the ground state vibrational interval, ΔG"(1/2), are reported for the five most abundant isotopomers. For the most abundant species, (90)Zr(56)Fe (47.2%), these values are: T(0) = 13931.9(1.2) cm(-1), ω'(e) = 325.05(54) cm(-1), ω'(e)x'(e) = 1.589(40) cm(-1), and ΔG"(1/2) = 452.2 cm(-1). Rotationally resolved studies have revealed ground and excited state rotational constants and Ω values, bond lengths and rotation-vibration constants, giving B(0)" = 0.138786(30) cm(-1) and r(0)" = 1.87685(20) Å for (90)Zr(56)Fe. The ground state and all observed excited states have Ω = 0. On the basis of the short bond length, the ground state of ZrFe is assigned as a nominally sextuply bonded (1)Σ(+) (Ω = 0(+)) state deriving from the 1σ(2)1π(4)2σ(2)1δ(4) electronic configuration. Above 18000 cm(-1), the spectrum becomes much more intense and congested, indicating the onset of electronically allowed transitions in this region.

Analytical approach for the excited-state Hessian in time-dependent density functional theory: Formalism, implementation, and performance

The paper presents the formalism, implementation, and performance of the analytical approach for the excited-state Hessian in the time-dependent density functional theory (TDDFT) that extends our previous work [J. Liu and W. Z. Liang, J. Chem. Phys. 135, 014113 (2011)] on the analytical Hessian in TDDFT within Tamm-Dancoff approximation (TDA) to full TDDFT. In contrast to TDA-TDDFT, an appreciable advantage of full TDDFT is that it maintains the oscillator strength sum rule, and therefore yields more precise results for the oscillator strength and other related physical quantities. For the excited-state harmonic vibrational frequency calculation, however, full TDDFT does not seem to be advantageous since the numerical tests demonstrate that the accuracy of TDDFT with and without TDA are comparable to each other. As a common practice, the computed harmonic vibrational frequencies are scaled by a suitable scale factor to yield good agreement with the experimental fundamental frequencies. Here we apply both the optimized ground-state and excited-state scale factors to scale the calculated excited-state harmonic frequencies and find that the scaling decreases the root-mean-square errors. The optimized scale factors derived from the excited-state calculations are slightly smaller than those from the ground-state calculations.

Electronic spectroscopy of CoNe+ via mass-selected photodissociation

The CoNe(+) diatomic cation is produced by laser vaporization in a pulsed-nozzle source and studied with photodissociation spectroscopy at visible wavelengths. Vibronic structure is assigned to the (3)Π(2) ← (3)Δ(3) band system correlating to the Co(+)((3)P(2) ← (3)F(4)) + Ne asymptote. The origin band (13,529 cm(-1)) and a progression of 14 other vibrational bands are detected ending in the dissociation limit at 14,191 cm(-1). The excited state dissociation energy is therefore D(0)(') = 662 cm(-1), and an energetic cycle using this, the origin band energy, and the atomic transition produces a ground state dissociation energy of D(0)(") = 930 cm(-1). The excited state vibrational frequency is 116.1 cm(-1). A rotationally resolved study of the origin band confirms the electronic transition assignment and provides the bond distance of r(0)(") = 2.36 Å. The properties of CoNe(+) are compared to those of other CoRG(+) and MNe(+) complexes studied previously.

Excited-state geometries and vibrational frequencies studied using the analytical energy gradients of the direct symmetry-adapted cluster–configuration interaction method. I. HAX-type molecules

In this series of studies, we systematically apply the analytical energy gradients of the direct symmetry-adapted cluster-configuration interaction singles and doubles nonvariational method to calculate the equilibrium geometries and vibrational frequencies of excited and ionized states of molecules. The harmonic vibrational frequencies were calculated using the second derivatives numerically computed from the analytical first derivatives and the anharmonicity was evaluated from the three-dimensional potential energy surfaces around the local minima. In this paper, the method is applied to the low-lying valence singlet and triplet excited states of HAX-type molecules, HCF, HCCl, HSiF, HSiCl, HNO, HPO, and their deuterium isotopomers. The vibrational level emission spectra of HSiF and DSiF and absorption spectra of HSiCl and DSiCl were also simulated within the Franck-Condon approximation and agree well with the experimental spectra. The results show that the present method is useful and reliable for calculating these quantities and spectra. The change in geometry in the excited states was qualitatively interpreted in the light of the electrostatic force theory. The effect of perturbation selection with the localized molecular orbitals on the geometrical parameters and harmonic vibrational frequencies is also discussed.

Analytical Hessian of electronic excited states in time-dependent density functional theory with Tamm-Dancoff approximation

We present the analytical expression and computer implementation for the second-order energy derivatives of the electronic excited state with respect to the nuclear coordinates in the time-dependent density functional theory (TDDFT) with Gaussian atomic orbital basis sets. Here, the Tamm-Dancoff approximation to the full TDDFT is adopted, and therefore the formulation process of TDDFT excited-state Hessian is similar to that of configuration interaction singles (CIS) Hessian. However, due to the replacement of the Hartree-Fock exchange integrals in CIS with the exchange-correlation kernels in TDDFT, many quantitative changes in the derived equations are arisen. The replacement also causes additional technical difficulties associated with the calculation of a large number of multiple-order functional derivatives with respect to the density variables and the nuclear coordinates. Numerical tests on a set of test molecules are performed. The simulated excited-state vibrational frequencies by the analytical Hessian approach are compared with those computed by CIS and the finite-difference method. It is found that the analytical Hessian method is superior to the finite-difference method in terms of the computational accuracy and efficiency. The numerical differentiation can be difficult due to root flipping for excited states that are close in energy. TDDFT yields more exact excited-state vibrational frequencies than CIS, which usually overestimates the values.

Efficient time-dependent density functional theory approximations for hybrid density functionals: Analytical gradients and parallelization

In this paper, we present the implementation of efficient approximations to time-dependent density functional theory (TDDFT) within the Tamm-Dancoff approximation (TDA) for hybrid density functionals. For the calculation of the TDDFT/TDA excitation energies and analytical gradients, we combine the resolution of identity (RI-J) algorithm for the computation of the Coulomb terms and the recently introduced "chain of spheres exchange" (COSX) algorithm for the calculation of the exchange terms. It is shown that for extended basis sets, the RIJCOSX approximation leads to speedups of up to 2 orders of magnitude compared to traditional methods, as demonstrated for hydrocarbon chains. The accuracy of the adiabatic transition energies, excited state structures, and vibrational frequencies is assessed on a set of 27 excited states for 25 molecules with the configuration interaction singles and hybrid TDDFT/TDA methods using various basis sets. Compared to the canonical values, the typical error in transition energies is of the order of 0.01 eV. Similar to the ground-state results, excited state equilibrium geometries differ by less than 0.3 pm in the bond distances and 0.5° in the bond angles from the canonical values. The typical error in the calculated excited state normal coordinate displacements is of the order of 0.01, and relative error in the calculated excited state vibrational frequencies is less than 1%. The errors introduced by the RIJCOSX approximation are, thus, insignificant compared to the errors related to the approximate nature of the TDDFT methods and basis set truncation. For TDDFT/TDA energy and gradient calculations on Ag-TB2-helicate (156 atoms, 2732 basis functions), it is demonstrated that the COSX algorithm parallelizes almost perfectly (speedup ~26-29 for 30 processors). The exchange-correlation terms also parallelize well (speedup ~27-29 for 30 processors). The solution of the Z-vector equations shows a speedup of ~24 on 30 processors. The parallelization efficiency for the Coulomb terms can be somewhat smaller (speedup ~15-25 for 30 processors), but their contribution to the total calculation time is small. Thus, the parallel program completes a Becke3-Lee-Yang-Parr energy and gradient calculation on the Ag-TB2-helicate in less than 4 h on 30 processors. We also present the necessary extension of the Lagrangian formalism, which enables the calculation of the TDDFT excited state properties in the frozen-core approximation. The algorithms described in this work are implemented into the ORCA electronic structure system.