Excited State Vibrational Frequencies Research Articles

Analytical energy gradients of Coulomb‐attenuated time‐dependent density functional methods for excited states

AbstractWe present an implementation and validation of the analytical energy gradient of time‐dependent density functional theory (TDDFT) using Coulomb‐attenuated (CA) functionals for excited state energies, dipole moments, geometries, and vibrational frequencies. The CA‐TDDFT gradient is based on the previous long‐range corrected TDDFT of (Chiba et al. J Chem Phys 2006, 124, 144106) and the Z‐vector formalism of (Furche and Ahlrichs J Chem Phys 2002, 117, 7433). Geometry optimization using CA‐TDDFT was carried out for molecules (substituted stilbenes and coumarins) having intramolecular charge‐transfer excited states and for a series of small molecules (CO, HCN, CH2O, CH2S, CCl2, C2H2, trans‐(CHO)2). We assess the results of the CA functionals, the long‐range corrected LC‐BLYP functional, and the B3LYP hybrid functional, by comparing to accurate experimental data. The results highlight the applicabilty of different functionals for excited state properties. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2010

Analysis of the excited-state absorption spectral bandshape of oligofluorenes

We present ultrafast transient absorption spectra of two oligofluorene derivatives in dilute solution. These spectra display a photoinduced absorption band with clear vibronic structure, which we analyze rigorously using a time-dependent formalism of absorption to extract the principal excited-state vibrational normal-mode frequencies that couple to the electronic transition, the configurational displacement of the higher-lying excited state, and the reorganization energies. We can model the excited-state absorption spectrum using two totally symmetric vibrational modes with frequencies 450 (dimer) or 400 cm(-1) (trimer), and 1666 cm(-1). The reorganization energy of the ground-state absorption is rather insensitive to the oligomer length at 230 meV. However, that of the excited-state absorption evolves from 58 to 166 meV between the oligofluorene dimer and trimer. Based on previous theoretical work [A. Shukla et al., Phys. Rev. B 67, 245203 (2003)], we assign the absorption spectra to a transition from the 1B(u) excited state to a higher-lying mA(g) state, and find that the energy of the excited-state transition with respect to the ground-state transition energy is in excellent agreement with the theoretical predictions for both oligomers studied here. These results and analysis permit profound understanding of the nature of excited-state absorption in pi-conjugated polymers, which are the subject of general interest as organic semiconductors in the solid state.

Recent Advances in Explicitly Correlated Coupled-Cluster Response Theory for Excited States and Optical Properties

Abstract The derivation of coupled-cluster response theory for explicitly correlated wavefunctions with terms linear in the interelectronic distance r 12 (CC-R12) or a function f 12 thereof (CC-F12) is reviewed and an implementation at the CCSD(R12) and CCSD(F12) for excitation energies and the linear, quadratic and cubic reponse functions is reported for ansätze 1 and 2. We discuss the results of first applications for vertical excitation energies, excited state equilibrium structures and vibrational frequencies, polarizabilities and first and second hyperpolarizabilities with focus on present limitations and future prospects of the approach. We show in particular that the standard choice of the geminal functions and wavefunction expansion can in certain cases lead to a bias towards the unperturbed ground state and how this can be avoided by extending the geminal space. If taken care of this, in particular CCSD(F12)/ansatz 2 shows for the potential energy curves of excited states and for optical properties a similar enhanced basis set convergence of the correlation contribution due to connected double excitations as for ground state energies. For diffuse excited states and hyperpolarizbilities the correlation contribution converges with CCSD(F12)/ansatz 2 often faster than orbital relaxation contributions. The convergence of the latter can be improved by allowing single excitations into a space spanned by a complementary auxiliary basis set.

The role of the methyl group in stabilising the weak N–H⋯π hydrogen bond in the 4-fluorotoluene–ammonia complex

The 4-fluorotoluene-ammonia van der Waals complex has been studied using a combination of resonant two-photon ionisation (R2PI) spectroscopy, ab initio molecular orbital calculations and multidimensional Franck-Condon analysis. The R2PI spectrum shows two sets of features assignable to two distinct conformers: one in which the ammonia binds between the hydrogen meta to the methyl group and the fluorine atom in a planar configuration and the other a pi-bound structure involving one bond between an ammonia hydrogen and the pi-system and another between the ammonia lone pair and the slightly acidic hydrogens on the methyl group. Ground state estimated CCSD(T) interaction energies were computed at the basis-set limit: these calculations yielded very similar interaction energies for the two conformers, whilst zero point energy correction yielded a zero point binding energy for the pi-complex about 10% larger than that of the in-plane, sigma-complex. The results of multidimensional Franck-Condon simulations based on ab initio ground and excited state geometry optimisations and vibrational frequency calculations showed good agreement with experiment, with further improvements achieved using a fitting procedure. The observation of a pi-complex in addition to a sigma-complex supports the intuitive expectation that electron-donating groups should help to increase pi-density and hence stabilise pi-proton acceptor complex formation. In this case, this occurs in spite of the presence of a strongly electron-withdrawing fluorine atom.

Heavy atom nitroxyl radicals. IV. Experimental and theoretical studies of the F2P=S free radical in the gas phase

The difluorothiophosphoryl (F(2)PS) free radical has been produced in a supersonic discharge jet from a precursor mixture of F(3)PS and high pressure argon and detected by laser-induced fluorescence and single vibronic level emission spectroscopy. With the aid of high level ab initio predictions of the properties of the ground and first two excited doublet states, the observed band system has been positively identified as B(2)A(')-X(2)A('). The electronic transition involves promotion of an electron from the pi to the pi( *) orbital with concomitant increases in the out-of-plane angle and PS bond length on excitation. The observed vibrational structure, Franck-Condon profile, rotational band contours, T(0) energy, and ground and excited state vibrational frequencies are all in accord with expectations based on our theoretical predictions.

Ultrafast Infrared Spectroscopy of Riboflavin: Dynamics, Electronic Structure, and Vibrational Mode Analysis

Femtosecond time-resolved infrared spectroscopy was used to study the vibrational response of riboflavin in DMSO to photoexcitation at 387 nm. Vibrational cooling in the excited electronic state is observed and characterized by a time constant of 4.0 +/- 0.1 ps. Its characteristic pattern of negative and positive IR difference signals allows the identification and determination of excited-state vibrational frequencies of riboflavin in the spectral region between 1100 and 1740 cm (-1). Density functional theory (B3LYP), Hartree-Fock (HF) and configuration interaction singles (CIS) methods were employed to calculate the vibrational spectra of the electronic ground state and the first singlet excited pipi* state as well as respective electronic energies, structural parameters, electronic dipole moments and intrinsic force constants. The harmonic frequencies of the S 1 excited state calculated by the CIS method are in satisfactory agreement with the observed band positions. There is a clear correspondence between computed ground- and excited-state vibrations. Major changes upon photoexcitation include the loss of the double bond between the C4a and N5 atoms, reflected in a downshift of related vibrations in the spectral region from 1450 to 1720 cm (-1). Furthermore, the vibrational analysis reveals intra- and intermolecular hydrogen bonding of the riboflavin chromophore.

Conformation and laser-induced fluorescence spectroscopy of phenetole in supersonic jet

Laser-induced fluorescence excitation and dispersed fluorescence spectra of phenetole have been measured in a cold supersonic jet expansion. The spectral features reveal the presence of only one conformer of the molecule in the environment of the jet, and the finding is consistent with the quantum chemistry predicted relative stability and conformational isomerization barriers of different isomers. The vibronic bands in the dispersed fluorescence spectra have been assigned fully with the aid of the normal mode frequencies predicted by density functional theoretical calculation. The geometry in the S 1 state has been optimized and the excited state vibrational frequencies have been calculated by CASSCF method. The theoretical results have been used to interpret the measured spectra.

High Resolution Spectral Differentiation of Enantiomers: Benzo[a]Pyrene Tetrols Complexed with a Promiscuous Antibody

The interaction of the highly cross-reactive anti-PAH monoclonal antibody with four diastereomeric benzo[a]pyrene tetrols (BPTs) is studied by means of fluorescence line-narrowing spectroscopy. It is shown that the interaction of enantiomers of cis-BPT and trans-BPT with the antibody involves different complex geometries. These spatially different ligand-protein interactions alter the relative intensities of the excited-state vibrational frequencies of immunocomplexed molecules allowing for unambiguous spectroscopic resolution of all four enantiomeric isomers. This study represents the first example of a high-resolution, fluorescence-based spectroscopic method capable of enantiospecific differentiation.

Ab initio predictions of the spectroscopic parameters of the germanium halomethylidyne (Ge=C-X; X=F, Cl, Br) free radicals

Ab initio methods have been used to predict the spectroscopic parameters for the X ˜ 2 Π i and A ˜ 2 Σ + states of the unknown germanium halomethylidyne (GeCX, X=F, Cl, Br) free radicals. The predictive powers of the chosen ab initio methods have been tested on the known GeCH radical. The calculations show the linear Ge CX (X=F, Cl, Br) isomer is the global minimum on the potential energy surface, with the cyclic XGeC isomer being between 6400 (BrGeC) and 11300 (FGeC) cm −1 higher in energy. The ground state geometries, vibrational frequencies, spin-orbit coupling and Renner parameters have been calculated using the cc-pVTZ basis set. The excited state geometries, vibrational frequencies and excitation energies have also been calculated, and the rotational contours of the 0 0 0 bands have been simulated at medium resolution under jet-cooled conditions. These calculations will aid in the search of these unknown radicals.

Quantum chemical computation of the spectroscopic constants of the [formula omitted] states of CBrCl and its heat of formation

The relative energies of the X ˜ , a ˜ and A ˜ states of CBrCl and its atomization energy in the complete basis limit were determined by extrapolating (spin restricted) CCSD(T), MRCI and EOM-CCSD energies calculated with the aug-cc-pV xZ ( x = T, Q, 5) basis sets which were corrected for core-valence correlation, scalar relativistic and spin–orbit coupling effects. The geometries and vibrational frequencies were calculated at the B3LYP/cc-pVTZ density functional and CASPT2/cc-pVTZ levels of theory. The predicted heat of formation at 298 K is 68.0 ± 1.0 kcal mol −1. The calculated singlet excited state vibrational frequencies and A ˜ ← X ˜ excitation energy are in close agreement with experiment.

Analytic gradients for excited states in the coupled-cluster model CC2 employing the resolution-of-the-identity approximation

The derivation and implementation of excited state gradients is reported for the approximate coupled-cluster singles and doubles model CC2 employing the resolution-of-the-identity approximation for electron repulsion integrals. The implementation is profiled for a set of examples with up to 1348 basis functions and exhibits no I/O bottlenecks. A test set of sample molecules is used to assess the performance of the CC2 model for adiabatic excitation energies, excited state structure constants and vibrational frequencies. We find very promising results, especially for adiabatic excitation energies, though the need of a single-reference ground state and a single-replacement dominated excited state puts some limits on the applicability of the method. Its reliability, however, can always be tested on grounds of diagnostic measures. As an example application, we present calculations on the π*←π excited state of trans-azobenzene.

Singlet and Triplet Valence Excited States of Pyrimidine

The absorption spectrum of pyrimidine vapor at 75 °C in the region of the first singlet−triplet transition, encompassing hot bands of the first singlet−singlet transition, has been obtained and analyzed with the aid of extensive ab initio (EOM-CCSD, CASPT2, and CIS) and density functional (B3LYP and TD-B3LYP) vibrational analyses. The hot bands in these spectra give information about low-frequency vibrations, several of which are vibronically active but are not particularly effective at inducing intensity. Spectra obtained at 18 °C are also reported for up to 1100 cm-1 above the singlet−singlet origin. Several singlet−singlet hot bands have been reassigned, giving excited-state vibrational frequencies for some modes. The calculations provide not only quantitative verification of perceived vibronic coupling and other features of the experimental assignments but also detailed maps of the complex lowest singlet and triplet manifolds. This includes vertical and adiabatic excitation energies, relaxation energi...

Discovery of the optically forbidden S1–S transition of silylidene (H2C=Si)

The electronically forbidden à 1A2–X̃ 1A1 band system of jet-cooled silylidene (H2CSi and D2CSi) has been detected for the first time using laser-induced fluorescence (LIF) and stimulated emission pumping (SEP) techniques. The very weak, vibronically induced 401 and 301401 bands were detected by LIF along with the corresponding 601 and 301601 bands which gain intensity through excited state Coriolis coupling. SEP spectra, obtained by pumping the 000 band of the S2 state and stimulating transitions down to the S1 state through the allowed S2–S1 transition, revealed many more bands, including the 000 bands, which were studied at high resolution and rotationally analyzed. From the upper state rotational constants of H2CSi and D2CSi, the excited state structure was obtained as r0′ (SiC)=1.873(2) Å, r0′(CH)=1.099(5) Å, and θ0′(HCH)=113.9(3)°. The four lowest energy excited state vibrational frequencies of both isotopomers have also been determined. High level ab initio predictions of the ground and excited state properties of silylidene are also reported and found to be in good agreement with the experimentally determined values.

Adiabatic time-dependent density functional methods for excited state properties

This work presents theory, implementation, and validation of excited state properties obtained from time-dependent density functional theory (TDDFT). Based on a fully variational expression for the excited state energy, a compact derivation of first order properties is given. We report an implementation of analytic excited state gradients and charge moments for local, gradient corrected, and hybrid functionals, as well as for the configuration interaction singles (CIS) and time-dependent Hartree–Fock (TDHF) methods. By exploiting analogies to ground state energy and gradient calculations, efficient techniques can be transferred to excited state methods. Benchmark results demonstrate that, for low-lying excited states, geometry optimizations are not substantially more expensive than for the ground state, independent of the molecular size. We assess the quality of calculated adiabatic excitation energies, structures, dipole moments, and vibrational frequencies by comparison with accurate experimental data for a variety of excited states and molecules. Similar trends are observed for adiabatic excitation energies as for vertical ones. TDDFT is more robust than CIS and TDHF, in particular, for geometries differing significantly from the ground state minimum. The TDDFT excited state structures, dipole moments, and vibrational frequencies are of a remarkably high quality, which is comparable to that obtained in ground state density functional calculations. Thus, yielding considerably more accurate results at similar computational cost, TDDFT rivals CIS as a standard method for calculating excited state properties in larger molecules.

Ab initio predictions of the spectroscopic parameters of the silicon halomethylidyne (Si=C–X; X=F,Cl,Br) free radicals

Ab initio methods have been used to predict the spectroscopic parameters for the ground (X̃ 2Πi) and first (Ã 2Σ+) excited states of the unknown silicon halomethylidyne (SiCF, SiCCl, and SiCBr) free radicals. The predictive power of the chosen theoretical methods has been satisfactorily tested on the known SiCH radical. Calculations show that the linear Si=C–X species is the global minimum on the potential energy surface, with the bent X–Si=C isomer several thousand cm−1 higher in energy. For the ground states, the geometries, vibrational frequencies, spin–orbit coupling constants, and Renner–Teller parameters have been predicted at several levels of theory with three different basis sets. These results can be used to generate a set of ground-state vibrational energy levels which may be useful in assigning the emission spectra of the radicals. The excited state geometries, vibrational frequencies, and excitation energies have also been calculated and the rotational contours of the 000 bands have been simulated at medium resolution under jet-cooled conditions. These calculations have been employed in a successful search for the spectrum of the SiCCl radical.

LIF excitation spectra of 2,6-dicyanoaniline

2,6-Dicyanoaniline (DCA) reveals remarkably different physicochemical and spectral properties than other aniline derivatives. The infrared and Raman spectra for DCA in solid state and laser induced fluorescence (LIF) excitation spectra of vacuum jet cooled molecules have been investigated. The ground S 0 and the S 1 (B 2 ) excited state geometries, charge distributions and vibrational frequencies of DCA have been evaluated by ab initio calculations. The Dushinsky matrices have been applied for the mode correlation and assignments of the transition frequencies in LIF excitation spectra of DCA(NH 2 ) and DCA(ND 2 ). The intensity distributions in LIF excitation spectra were modeled. The dominant vibronic bands in the excitation spectra are connected with motions of the adjacent cyano- and amino groups. The transitions involving inversion motion of the amino group have low intensities.

Dispersed fluorescence spectroscopy of jet-cooled AgAu and Pt2

Dispersed fluorescence spectroscopy has been used to study jet-cooled AgAu and Pt2. Fluorescence resulting from the excitation of five bands of the A←X 1Σ+ system of AgAu was dispersed, and 51 measured ground state vibrational levels were fit to provide ground state vibrational constants of ωe″=198.22±0.11 cm−1 and ωe″xe″=0.512±0.002 cm−1. A Franck–Condon calculation was performed using the experimental values of the ground and excited state vibrational frequencies and anharmonicities, providing an estimate of the change in bond length upon excitation of the A←X system of Δre=0.214±0.005 Å. Fluorescence resulting from four different excitations of Pt2 was dispersed, providing vibrational constants for the ground and two low-lying excited states. Ground state vibrational constants of ωe=222.3 cm−1 and ωexe=0.62 cm−1 were obtained, based on the analysis of 16 measured ground state vibrational levels. In addition, a low-lying excited state was located at T0=2877 cm−1, with ωe=197 cm−1. This state perturbed the ground state, from which it was deduced that it has the same symmetry as the ground state. A comparison to theoretical calculations suggests that both states have 0g+ symmetry. Finally, a metastable state of Pt2 lying at an unknown energy was determined to have ωe=211 cm−1, ωexe=0.4 cm−1.

Spectroscopy of UO(2)Cl(4)(2)(-) in basic aluminum chloride-1-ethyl-3-methylimidazolium chloride.

The optical absorption, emission, FT Raman, one-photon excitation, two-photon excitation, and luminescence lifetime measurements are reported for UO(2)Cl(4)(2)(-) in 40:60 AlCl(3)-EMIC (where EMIC identical with 1-ethyl-3-methylimidazolium chloride), a room-temperature ionic liquid. Comparison of the spectra with previous results from single crystals containing UO(2)Cl(4)(2)(-) allowed the characterization of four ground-state vibrational frequencies, two excited-state vibrational frequencies, and the location of eight electronic excited-state energy levels. The vibrational frequencies and electronic energy levels are found to be consistent with the UO(2)Cl(4)(2)(-) ion. Comparison of the one-photon and two-photon excitation spectra, and the relative intensities of the transitions in the emission spectrum indicate that the center of symmetry is perturbed by an interaction with the solvent.

Spectroscopic detection and characterization of iodogermylene (HGel)

Monoiodogermylene has been detected for the first time using pulsed discharge and laserinduced fluorescence techniques. HGeI and DGeI were produced by an electric discharge through argon seeded with H3GeI or D3GeI. Although the vibronic structure in the spectra was very limited, all three excited state vibrational frequencies have been obtained for both isotopomers. Analysis of the partially resolved rotational structure of the 000 bands gave the following approximate r0 structures, with the bond angles constrained to previous ab initio values: r0″(Ge–I)=2.525(10) Å, r0″(H–Ge)=1.593(15) Å, θ0″(HGeI)=93.5°, r0′(Ge–I)=2.515(10) Å, r0′(H–Ge)=1.618(15) Å, and θ0′(HGeI)=116.2°. The fluorescence lifetime of monoiodogermylene in the lowest rovibronic levels is 1.515±0.004 μs and shows significant variations on deuteration and with rotational and vibrational level.

The electronic spectrum of monoiodosilylene (HSiI) revisited

The à 1A″–X̃ 1A′ spectra of jet-cooled HSiI and DSiI have been studied using the pulsed discharge technique, using H3SiI and D3SiI as precursors. The excited state vibrational frequencies have been determined and the literature value of ν1′ substantially revised. Although a reliable excited state equilibrium structure was unattainable, the rotational constants of the 000 bands gave the structural parameters r0″(Si–I)=2.463(1) Å, r0″(Si–H)=1.534(1) Å, θ0″(HSiI)=92.4(1)°, r0′(Si–I)=2.436(1) Å, r0′(Si–H)=1.515(5) Å, and θ0′(HSiI)=114.9(2)°. The radiative lifetime of the 000 band has been measured to be 1230±30 ns. Trends in the structural parameters, vibrational frequencies, and their changes on electronic excitation for the monohalosilylenes have been discussed.