Ground State Normal Modes Research Articles

Role of Explicit Solvation in the Simulation of Resonance Raman Spectra within Short-Time Dynamics Approximation.

In short-time dynamics approximation, relative resonance Raman (RR) intensity of a vibrational mode primarily depends on the magnitude of square of the excited-state gradient along the corresponding normal coordinate, ground-state normal mode eigenvector, and harmonic vibrational wavenumbers. In this study, through simulation of RR spectra of guanosine-5'-monophosphate (GMP) in two ππ* singlet excited states, we analyze how the explicitly hydrogen-bonded local solvation structure of the chromophore dictates intensities of the RR active modes in an unprecedented manner. We show that the accuracy of the structural model of solvated chromophore plays a decisive role in determining an optimal theoretical method for prediction of the Franck-Condon region of the ππ* excited states. 9-Methylguanine (9-meG) in complex with six water molecules (9-meG·6H2O) is found out to be the most accurate one for describing GMP in two different bright electronic states. We find that explicit hydrogen-bonded water molecules strongly influence computed RR intensities of GMP by modulating both the ground-state normal mode vectors and the excited-state energy gradients. We find that simultaneous inclusion of six explicit waters to describe the solute-solvent interaction near all hydration sites is essential for reliable prediction of the features of RR spectra in Lb and Bb electronic states of GMP.

Simulation of Impulsive Vibrational Spectroscopy.

In the present work we applied a fully atomistic electron-nuclear real-time propagation protocol to compute the impulsive vibrational spectroscopy of the five DNA/RNA nucleobases in order to study the very first steps (subpicosecond) of their energy distribution after UV excitation. We observed that after the pump pulse absorption the system is prepared in a coherent superposition of the ground and the pumped electronic excited states in the equilibrium geometry of the ground state. Furthermore, for relatively low fluency values of the pump pulse, the dominant contribution to the electronic wave function of the coherent state is of the ground state and the mean potential energy surface within the Ehrenfest approximation is similar to that of the ground state. As a consequence, the molecular displacements are better correlated with ground-state normal modes. On the other hand, when the pump fluency is increased the excited-state contribution to the electronic wave function becomes more important and the mean potential energy surface resembles more that of the excited state, producing a better correlation between the molecular displacements and the excited-state normal modes. Finally, it has been observed that the impulsive activation of several vibrational modes upon electronic excitation is triggered by the development of excited-state forces which accelerate the nuclei from their equilibrium positions causing a distribution of the absorbed electronic energy on the nuclear degrees of freedom and could be closely related to the driving force of the ultrafast nonradiative deactivation observed in these systems.

Effects of hydrogen bonding with H2O on the resonance Raman spectra of uracil and thymine

The effects of explicit hydrogen bonding with H2O on the resonance Raman spectra of uracil and thymine are examined computationally. The three bonding sites in uracil and thymine that form the lowest energy uracil-H2O and thymine-H2O complexes, as well as a more limited number of low-lying ones containing two waters, are considered. The ground state structures are optimized at the PBE0/aug-cc-pVTZ level of theory in H2O (C-PCM), and the gradients of the bright excited state (S1) are computed at the TD-CAM-B3LYP/aug-cc-pVTZ level of theory in H2O (C-PCM). As the resonance Raman spectrum is governed by the ground state normal modes and the excited state Cartesian gradient (within the Herzberg-Teller formalism), the differences between spectra of uracil- and thymine-(H2O)n, n=1 or 2, are compared in terms of these two factors. Explicit hydrogen bonding to water is found to cause changes in both relative peak positions and intensities for the resonance Raman spectra of uracil and thymine when compared to the isolated molecules. The effect of hydrogen bonding is primarily on the ground state normal mode character, especially for the high frequency modes (>1600cm−1), rather than on the excited state Cartesian gradients. Different hydrogen bonding sites are found to have different contributions to the resulting resonance Raman spectra, and inclusion of explicit hydrogen bonding on the carbonyl bond opposite to the ring nitrogen is necessary to obtain good agreement between the simulated and experimental resonance Raman spectra for uracil and thymine.

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.

The problem of hole localization in inner-shell states of N2 and CO2 revisited with complete active space self-consistent field approach

Potential energy curves for inner-shell states of nitrogen and carbon dioxide molecules are calculated by inner-shell complete active space self-consistent field (CASSCF) method, which is a protocol, recently proposed, to obtain specifically converged inner-shell states at multiconfigurational level. This is possible since the collapse of the wave function to a low-lying state is avoided by a sequence of constrained optimization in the orbital mixing step. The problem of localization of K-shell states is revisited by calculating their energies at CASSCF level based on both localized and delocalized orbitals. The localized basis presents the best results at this level of calculation. Transition energies are also calculated by perturbation theory, by taking the above mentioned MCSCF function as zeroth order wave function. Values for transition energy are in fairly good agreement with experimental ones. Bond dissociation energies for N(2) are considerably high, which means that these states are strongly bound. Potential curves along ground state normal modes of CO(2) indicate the occurrence of Renner-Teller effect in inner-shell states.

Application of an efficient multireference approach to free-base porphin and metalloporphyrins: Ground, excited, and positive ion states

The improved virtual orbital-complete active space configuration interaction (IVO-CASCI) method is applied to determine the geometries of the ground state of free-base porphin and its metal derivatives, magnesium and zinc porphyrins. The vertical excitation energies and ionization potentials are computed at these optimized geometries using an IVO-based version of multireference Möller-Plesset (IVO-MRMP) perturbation theory. The geometries and excitation energies obtained from the IVO-CASCI and IVO-MRMP methods agree well with experiment and with other correlated many-body methods. We also provide the ground state vibrational frequencies for free-base porphin and Mg-porphyrin. All frequencies are real in contrast to self-consistent field treatments which yield an imaginary frequency. Ground state normal mode frequencies (scaled) of free-base porphin and magnesium porphyrin from IVO-CASCI and complete active space self-consistent field methods are quite similar and are consistent with Becke-Slater-Hartree-Fock exchange and Lee-Yang-Parr correlation density functional theory calculations and with experiment. In addition, geometries are determined for low-lying excited state triplets and for positive ion states of the molecules. To our knowledge, no prior experimental and theoretical data are available for these excited state geometries of magnesium and zinc porphyrins. Given that the IVO-CASCI and IVO-MRMP computed geometries and excitation energies agree favorably with experiment and with available theoretical data, our predicted excited state geometries should be equally accurate.

Resonance Raman study of the solvent dynamics for ultrafast charge transfer transition in 4-nitro-4′-dimethylamino-azobenzene

Contribution of solvent reorganization energy is known to be significant for ultrafast charge transfer processes, when the solvent relaxation times are slower than the rate of charge transfer. In this paper, we show that from resonance Raman intensities of a charge transfer transition in combination with Heller’s time-dependent wave packet approach and Brownian oscillator model, one can have a reasonable estimate for the different types of solvent (inertial as well as diffusive) and vibrational reorganization energies. Resonance Raman spectra have been recorded for 4-nitro-4′-dimethylamino-azobenzene (DA) that undergoes photoinduced charge transfer transition, in acetonitrile and benzonitrile. In the two solvents, the total solvent reorganization energy is partitioned into its inertial and diffusive components from the available information on their relaxation time scales. Thus, partitioning of the solvent reorganization energy reveals the importance of the extent of contribution of the two components to the charge transfer rates. The short time dynamics of DA in the two solvents is then examined from a priori knowledge of the ground state normal modes in order to convert the wave packet motion in dimensionless displacements to internal coordinates. The dynamics in DA infers that within 20 fs after photoexcitation from the ground to the charge transfer state, the excited state evolution occurs along N–O, N=N, C–N, and C–C stretching vibrations.

Vibrational and structural analysis of the radical cation of N,N,N′,N′-tetramethylbenzidine based on ab initio calculations and time-resolved resonance Raman spectroscopyElectronic supplementary information (ESI) available: Potential energy distributions (PED) expressed in terms of the local symmetry coordinates for each isotopomer (Table 1S and 3S); description of the symmetry coordinates (Table 2S) and related internal coordinates (Fig. 1S). See http://www.rsc.org/suppdata/cp/b2/b210837m/

New time-resolved resonance Raman spectra of the radical cation of N,N,N′,N′-tetramethylbenzidine (TMB) in solution have been probed at 752 nm, in resonance with a strong electronic transition, for several isotopic derivatives. These spectra and those obtained previously at 488 nm, in resonance with a second electronic transition, have been interpreted by means of the density functional theory (B3LYP) calculations. An unambiguous assignment of the observed vibrations has been deduced. For comparison, similar calculations have been done for the parent ground state molecule. In addition, configuration interaction singles (CIS) calculations have been used to assign the two resonant electronic excited states of the radical cation and identify the molecular orbitals involved in the corresponding transitions. On this basis, the Raman intensities of the radical cation in resonance with these two transitions have been evaluated in the Franck–Condon approximation by projecting the excited state potential energy surface gradients, determined from CASSCF calculations, on the ground state normal modes. The analysis of both the vibrational frequencies and resonance Raman intensities suggests that the TMB radical cation adopts a coplanar structure (D2h point group).

Resonance Raman Spectra Simulation of the 4,4‘-Bipyridine Anion Radical and N-Protonated Radical

A low-cost computational methodology is utilized to calculate the resonance Raman spectra of the 4,4‘-bipyridine anion radical (44BPY-•) and N-hydro radical (44BPYH•). The resonance Raman intensities are evaluated in the Franck−Condon approximation, by projecting the excited state surface gradient (calculated with the CASSCF method) on the ground state normal modes (determined at ROHF level of theory). TD-DFT and CIS calculations are used to assign the resonant electronic states, estimate the intensity and excitation energy of the related transitions, and identify the molecular orbitals involved in these transitions. These molecular orbitals are then used to construct CASSCF active spaces as small as possible and to compute the excited-state gradients. The results appear to be very satisfactory for 44BPY-• and reasonable for 44BPYH•. They allow identifying the nature of the probed resonant electronic transitions of these transient species and provide a precise picture of their electronic configuration. A comparative analysis of these results and those reported previously for the lowest excited S1 state of 44BPY reveals a clear analogy of the electronic structures of the N-hydro radical and excited S1 state.

Molecular Orbital Study of the First Excited State of the OLED Material Tris(8-hydroxyquinoline)aluminum(III)

Tris(8-hydroxyquinoline)aluminum(III), Alq3, is used in organic light-emitting diodes (OLEDs) as an electron transport material and emitting layer. The lowest singlet excited state (S1) of Alq3 has been studied by the singles configuration interaction (CIS) method and time-dependent density functional theory (TD-DFT) using a hybrid functional, B3-LYP, and the 3-21+G** basis set. For comparison and calibration, 8-hydroxyquinoline has also been examined with these methods using the 3-21+G** and larger basis sets. The lowest singlet electronic transition (S0 → S1) of Alq3 is primarily localized on one of the quinolate ligands. Comparison of the CIS optimized excited-state structure and the Hartree−Fock ground-state structure indicates that the geometric shift is mainly confined to the a-quinolate. Very similar changes are found for the S1 state of 8-hydroxyquinoline, and these changes can be easily understood in terms of the nodal patterns of the highest occupied and lowest unoccupied molecular orbitals. The structural relaxation upon excitation, when expressed in terms of ground-state normal modes of vibration, corresponds to a quinolate skeletal vibrational mode at 534 cm-1 and serves to assign the vibronic structure observed in the low-temperature emission spectra. On the basis of the CIS-optimized structure of the excited state, TD-B3-LYP calculations predict an emission wavelength of 538 nm, which is comparable to 514 nm observed experimentally for solution phase photoluminescence. The Stokes shift calculated by TD-B3-LYP is 123 nm, in excellent agreement with the observed value of 126 nm.

Symmetry breaking effects in NO3−: Raman spectra of nitrate salts and ab initio resonance Raman spectra of nitrate–water complexes

Ground-state structures and vibrational frequencies are calculated for complexes of the nitrate anion with one and two water molecules at the ab initio Hartree–Fock level with a basis set including diffuse and polarization functions. Two local minimum geometries are found for each complex. Calculations of the electronically excited states at the CIS level are then used to find the forces on each of the atoms upon vertical excitation to the two lowest-lying (near-degenerate) strongly allowed electronic transitions. These forces are converted to gradients of the excited-state potential surfaces along the ground-state normal modes and compared with the parameters obtained previously from empirical simulations of the experimental resonance Raman intensities of NO3− in dilute aqueous solution. The calculations on two-water clusters agree well with the experimental excited-state geometry changes along the totally symmetric N–O stretch. The calculations underestimate the frequency splitting of the antisymmetric stretching vibration (degenerate in the isolated D3h ion) and the resonance Raman intensity in this mode, suggesting that bulk solvent polarization enhances the asymmetry of the local environment for NO3− in water. Comparison of the ground-state vibrational frequency splitting of the antisymmetric stretch with the corresponding values for the nitrate ion in salts having known crystal structures suggests that the rms difference among the three N–O bond lengths for nitrate anion in water probably exceeds 0.01 Å.

Ground state normal mode analysis: Linking excited state dynamics and experimental observables

Aspects of the photoinduced ring opening reaction of cyclohexadiene with subsequent relaxation to cZc-hexatriene or back to cyclohexadiene are investigated theoretically. In this ultrafast reaction the S1 state plays a central role, providing the possibility for the molecule to rapidly decay from the excited to the ground state via multiple conical intersections. To better understand the dynamics of the molecule on its way toward the product states, we perform a normal mode analysis of its vibrations in the vicinity of two prominent conical intersections and find several eigenmodes to characterize its motion. This raises hope that our findings could lead to an experimental scheme of detection for the wave packet motion in the hot product states by a time resolved transient absorption measurement. In the end this might be useful in designing an input signal for an optimal control experiment to selectively steer the molecule through a specific conical intersection and influence the product yield.

Molecular Vibrations of Pteridine and Two Symmetric Tetraazanaphthalenes

The molecular vibrations of 1,4,5,8-tetraazanaphthalene (1458-TAN), 2,3,6,7-tetraazanaphthalene (2367-TAN) and pteridine are analyzed using a combination of infrared and Raman spectroscopy, ab initio calculations at the HF/6-31G* and MP2/6-31G* levels of theory, and B3LYP/4-31G and B3LYP/6-31G* density-functional calculations. New spectra are reported, and almost all of the ground-state normal modes have been identified for 1458-TAN and pteridine; the analysis for 2367-TAN is less complete. Calculated B3LYP/6-31G* vibrational frequencies provide the best correlation between theory and experiment for these compounds, but corresponding calculations using the smaller 4-31G basis are also satisfactory. The spectra of 1458-TAN and pteridine spectra exhibit a substantial number of Fermi resonances which complicate but do not prevent a detailed analysis.

Resonance Raman spectroscopy as a test ofab initio methods for the computation of molecular potential energy surfaces

The use of ab initio quantum chemical methods to aid in the interpretation of resonance Raman spectra is illustrated with examples where the resonant electronic absorption spectra are unstructured. In such cases only the gradient of the excited electronic state potential energy surface at the ground electronic state geometry is important in determining the upper state dynamics that are relevant to the Raman scattering process. The use of ab initio methods for which analytic gradients are available permits application to large molecular systems and to cluster models of molecules in solution. This procedure eliminates possible ambiguities in the empirical interpretation of resonance Raman spectra. These same ab initio methods may be used to provide descriptions of the ground-state normal modes and the effect of isotopic substitution on the form of the normal modes. © 1998 John Wiley & Sons Ltd.

Early time dynamics of trans-azobenzene isomerization in solution from resonance Raman intensity analysis

Resonance Raman spectra have been recorded for trans-azobenzene in carbon tetrachloride using 16 excitation wavelengths in the region from 355–600 nm. It has been observed that for many totally symmetric fundamentals viz. C–N, N=N stretch, etc., the resonance Raman intensities decrease near the maxima of the resonant electronic (2 1Ag←1 1Ag) transition. This is attributed to interference due to preresonant scattering from the strongly allowed (1 1Au←1 1Ag) electronic transition. The Raman excitation profiles (REPs) for the ten Franck–Condon active fundamentals have been successfully modeled using Heller’s time-dependent approach with the inclusion of interference effect from higher electronic state. The short time isomerization dynamics is then examined from a priori knowledge of ground-state normal mode descriptions to convert the wave packet motion in dimensionless normal coordinates to internal coordinates. It is observed that within 5–30 fs of photoexcitation, the major changes experienced by trans-azobenzene are on N=N and C–N stretching vibrations, while N=N suffers reduction, C–N bond elongates, and with time the ring C atoms distort relatively out of the plane.

Modeling the Soret-Resonant Raman Intensities of Metalloporphyrins and Heme Proteins. 1. Nickel Porphine

A framework is developed for modeling the resonance Raman (RR) intensities of metalloporphyrins, with a view toward rationalizing the enhancement patterns observed in the spectra of heme proteins. The geometry of the S2 excited state of nickel(II) porphine is computed using INDO/1s methods, and the structural changes resulting from S0−S2 photoexcitation are projected onto the ground-state normal modes to calculate the intensity of each Raman-active vibration. The RR intensities derive mainly from expansion of the CαCm and CβCβ bonds in the excited state, with the relative intensities strongly influenced by the phasing between CαCm and CβCβ stretching coordinates. Analysis of the ν8 overtone shows the INDO predicted geometry changes to be about 25% too large. Results are compared at successive levels of approximation, demonstrating that inclusion of displacements along bending coordinates in the excited state are essential, as are frequency-dependent scaling factors which are determined from the absorption...

Ab initio calculations of vibronic spectra for indole

Detailed vibronic fluorescence spectra from the 1L b and 1L a state origins of indole are computed from the geometry differences and ground state normal modes determined by GAUSSIAN 92 and a program to calculate Franck-Condon factors. The combination of using CIS/3-21G and HF/3-21G basis sets for excited and ground state geometries and MP2/6-31G ∗ for the ground state vibrational modes captures many subtle details seen in the experimental 1L b fluorescence.

Studies of the Vibrational and Electronic Structure of the S1 Excited States of .beta.-Substituted Porphyrins by Picosecond Time-Resolved Resonance Raman Spectroscopy

Resonance Raman (RR) spectra are reported for the S{sub 1} excited states of zinc(II) complexes of octaethylporphyrin (OEP) and protoporphyrin-IX-dimethyl ester (PPDME). Skeletal stretching modes exhibit large downshifts in the S{sub 1} state of ZnOEP relative to the ground state, indicating an overall expansion of the macrocycle upon photoexcitation. Vibrational modes are assigned using {sup 15}N and meso-d{sub 4} isotopomers of OEP: the isotopic sensitivity is observed to be similar in the S{sub 0} and S{sub 1} states, implying that the ground-state normal mode structure is preserved in the singlet excited state. Excited-state bond orders are calculated using INDO1/S methods. The frequency shift patterns for skeletal vibrational modes of ZnPPDME in the S{sub 1} excited state closely resemble those of ZnOEP, implying a similar electronic configuration; the vinyl C=C stretching mode appears to be only slightly perturbed in the excited states, although the exact position cannot be accurately determined. The results of these studies support the description of metalloporphyrin singlet excited states provided by Gouterman`s four-orbital model. 69 refs., 9 figs., 3 tabs.

ChemInform Abstract: INTERPRETATION OF CIS‐HEXATRIENE ABSORPTION SPECTRUM. THE DUSCHINSKY EFFECT

The differences between the uv absorption spectra of trans‐ and cis‐hexatriene are interpreted in terms of the coupling between the ground state normal modes in the electronic excited state, i.e., the Duschinsky effect. The model Hamiltonian is derived and its eigenvalues and eigenvectors are found by means of the standard perturbation theory. The spectra of both molecules are simulated at the computer. A good agreement with experiment is found. Some approximations involved are discussed and the possibilities of further experimental verification are pointed out.

Interpretation of c i s-hexatriene absorption spectrum. The Duschinsky effect

The differences between the uv absorption spectra of trans- and cis-hexatriene are interpreted in terms of the coupling between the ground state normal modes in the electronic excited state, i.e., the Duschinsky effect. The model Hamiltonian is derived and its eigenvalues and eigenvectors are found by means of the standard perturbation theory. The spectra of both molecules are simulated at the computer. A good agreement with experiment is found. Some approximations involved are discussed and the possibilities of further experimental verification are pointed out.