Excited Potential Energy Surfaces Research Articles

Exploring Nuclear Photorelaxation of Pyranine in Aqueous Solution: an Integrated Ab-Initio Molecular Dynamics and Time Resolved Vibrational Analysis Approach.

Advances in time-resolved vibrational spectroscopy techniques provided a new stimulus for understanding the transient molecular dynamics triggered by the electronic excitation. The detailed interpretation of such time-dependent spectroscopic signals is a challenging task from both experimental and theoretical points of view. We simulated and analyzed the transient photorelaxation of the pyranine photoacid in aqueous solution, with special focus on structural parameters and low frequency skeleton modes that are possibly preparatory for the photoreaction occurring at later time, as suggested by experimental spectroscopic studies. To this aim, we adopted an accurate computational protocol that combines excited state ab initio molecular dynamics within an hybrid quantum mechanical/molecular mechanics framework and a time-resolved vibrational analysis based on the Wavelet transform. According to our results, the main nuclear relaxation on the excited potential energy surface is completed in about 500 fs, in agreement with experimental data. The rearrangement of C-C bonds occurs according to a complex vibrational dynamics, showing oscillatory patterns that are out of phase and modulated by modes below 200 cm-1. We also analyzed in both the ground and the excited state the evolution of some structural parameters involved in excited state proton transfer reaction, namely, those involving the pyranine and the water molecule hydrogen bonded to the phenolic O-H group. Both the hydrogen bond distance and the intermolecular orientation are optimized in the excited state, resulting in a tighter proton donor-acceptor couple. Indeed, we found evidence that collective low frequency skeleton modes, such as the out of plane wagging at 108 cm-1 and the deformation at 280 cm-1, are photoactivated by the ultrafast part of the relaxation and modulate the pyranine-water molecule rearrangement, favoring the preparatory step for the photoreactivity.

Excited interatomic potential energy surfaces of Rb + He that correlate with Rb terms 52S through 72S.

The excited state interatomic potential energy surfaces for Rb + He are computed at the spin-orbit multi-reference configuration interaction level of theory using all-electron basis sets of triple and quadruple-zeta quality that have been contracted for Douglas-Kroll-Hess (DKH) Hamiltonian and includes core-valence correlation. Davidson-Silver corrections (MRCI+Q) are employed to ameliorate size consistency error. An extrapolation of CASSCF energies is performed using the procedure of Karton and Martin whereas extrapolation of correlation energy is performed using an expression involving the inverse powers of (lmax + 1/2), the highest angular momentum value present in the basis set. The spin-orbit energies in the limit of complete basis set are obtained by replacing the energy eigenvalues in the spin-orbit matrix by the relativistic-corrected MRCI+Q energies extrapolated to the complete basis set limit. MRCI diabatic potential energy surfaces for a few selected 2Σ states are calculated to study the general topology and avoided crossings and repulsive form of the 6s 2Σ+ state. Important features of the potential energy surfaces are discussed with implications for alkali laser spectroscopy.

Analytical derivatives of the individual state energies in ensemble density functional theory method. I. General formalism.

The state-averaged (SA) spin restricted ensemble referenced Kohn-Sham (REKS) method and its state interaction (SI) extension, SI-SA-REKS, enable one to describe correctly the shape of the ground and excited potential energy surfaces of molecules undergoing bond breaking/bond formation reactions including features such as conical intersections crucial for theoretical modeling of non-adiabatic reactions. Until recently, application of the SA-REKS and SI-SA-REKS methods to modeling the dynamics of such reactions was obstructed due to the lack of the analytical energy derivatives. In this work, the analytical derivatives of the individual SA-REKS and SI-SA-REKS energies are derived. The final analytic gradient expressions are formulated entirely in terms of traces of matrix products and are presented in the form convenient for implementation in the traditional quantum chemical codes employing basis set expansions of the molecular orbitals. The implementation and benchmarking of the derived formalism will be described in a subsequent article of this series.

Conformational Changes in 5-Methoxyindole: Effects of Thermal, Vibrational, and Electronic Excitations

The molecule of 5-methoxyindole (5MOI) may adopt two conformational states, syn and anti, with respect to the relative orientation of the NH and OCH3 groups. The structure of monomeric 5MOI was characterized spectroscopically, in mid- and near-infrared domains. The conformational composition of 5MOI could be controlled in three different ways. Thermally, two conformers of 5MOI could be trapped in xenon matrixes at 16 K. Upon annealing the xenon matrix to temperatures about 30-40 K, the higher-energy syn form converted to the ground-state anti conformer. Vibrational excitations in the near-infrared domain, at the frequency of the first NH stretching overtone, 6853 cm-1, afforded the inverse conformational transformation, and a part of the anti conformer was upconverted to the syn form. Electronic excitations in the UV domain, at 315-310 nm, resulted in a total consumption of the syn form again, in favor of anti. Upon further irradiations at 308 nm, a partial repopulation of the syn form, at the expense of anti, was observed. We propose a mechanistic explanation of the observed transformations, which is based on computations of the vibrational spectra of the two conformers and also on computations of the ground state S0 and the first excited state S1 potential energy surfaces along the coordinate for conformational isomerization. The highlights of the present work are the first experimental observation of the minor syn conformer of 5MOI, evidence of the long-range vibrational energy transfer resulting in conformational isomerization upon excitation of the NH stretching overtone, and the possibility of partial conformational control of 5MOI by using electronic excitations.

The Primary Photochemistry of Vision Occurs at the Molecular Speed Limit.

Ultrafast photochemical reactions are initiated by vibronic transitions from the reactant ground state to the excited potential energy surface, directly populating excited-state vibrational modes. The primary photochemical reaction of vision, the isomerization of retinal in the protein rhodopsin, is known to be a vibrationally coherent reaction, but the Franck-Condon factors responsible for initiating the process have been difficult to resolve with conventional time-resolved spectroscopies. Here we employ experimental and theoretical 2D photon echo spectroscopy to directly resolve for the first time the Franck-Condon factors that initiate isomerization on the excited potential energy surface and track the reaction dynamics. The spectral dynamics reveal vibrationally coherent isomerization occurring on the fastest possible time scale, that of a single period of the local torsional reaction coordinate. We successfully model this process as coherent wavepacket motion through a conical intersection on a ∼30 fs time scale, confirming the reaction coordinate as a local torsional coordinate with a frequency of ∼570 cm-1. As a result of spectral features being spread out along two frequency coordinates, we unambiguously assign reactant and product states following passage through the conical intersection, which reveal the key vibronic transitions that initiate the vibrationally coherent photochemistry of vision.

Coherent and incoherent structural dynamics in laser-excited antimony

We investigate the excitation of phonons in photoexcited antimony and demonstrate that the entire electron-lattice interactions, in particular coherent and incoherent electron-phonon coupling, can be probed simultaneously. Using femtosecond electron diffraction (FED) with high temporal resolution, we observe the coherent excitation of the fully symmetric \Ag\ optical phonon mode via the shift of the minimum of the atomic potential energy surface. Ab initio molecular dynamics simulations on laser excited potential energy surfaces are performed to quantify the change in lattice potential and the associated real-space amplitude of the coherent atomic oscillations. Good agreement is obtained between the parameter-free calculations and the experiment. In addition, our experimental configuration allows observing the energy transfer from electrons to phonons via incoherent electron-lattice scattering events. The electron-phonon coupling is determined as a function of electronic temperature from our DFT calculations and the data by applying different models for the energy-transfer.

Quasiclassical trajectory study of the C(1D) + HD reaction

Isotopic branching ratios are investigated by detailed quasiclassical trajectory calculations on our recent singlet ground and excited potential energy surfaces.

Theoretical illumination of highly original photoreactive 3MC states and the mechanism of the photochemistry of Ru(ii) tris(bidentate) complexes.

We have identified highly novel photoreactive 3MC states of ruthenium(ii) 4,4'-bi-1,2,3-triazolyl (btz) complexes of the form [Ru(N^N)(btz)2]2+ and have elucidated the mechanism of the highly unusual experimental observations of photochemical ligand dechelation and concomitant ligand rearrangement reactivity to form unusual photoproducts trans-[Ru(N^N)(κ2-btz)(κ1-btz)(solvent)]2+. The triplet metal-to-ligand charge-transfer (3MLCT) states and classical Jahn-Teller type triplet metal-centred (3MC) states of the series of complexes [Ru(N^N)3-n(btz)n]2+ (btz = 4,4'-bi-1,2,3-triazolyl; N^N = 2,2'-bipyridyl (bpy), n = 0 (1), 1 (2), 2 (3), 3 (5); N^N = 4-(pyrid-2-yl)-1,2,3-triazole (pytz), n = 1 (4)) have been optimised by density functional theory (DFT) and characterised. There is a gradual and significant destabilisation of the 3MLCT states as the triazole content of the complexes increases, which occurs with a slight stabilisation of the 3MC states. Whilst consistent with the promotion of photochemical reactivity in the heteroleptic complexes of the series relative to 1, these classical 3MC states fail to account for the extraordinary ligand rearrangement processes that accompany ligand ejection. Thorough theoretical exploration of the lowest excited triplet potential energy surface (3PES) here reveals the existence of a new type of 3MC state and the role it plays in the photochemical reactivity of the complexes. This newly discovered state, called MC(F), displays a flattened geometry (indicated by the 'F' in the parentheses) which makes it clearly on the path to achieving the coplanarity of the bidentate ligands in the experimentally observed trans-photoproduct. Further novel 'pentacoordinate' 3MC states with coplanar bidentate ligands, called MC(P) (where the 'P' in the parentheses denotes the pentacoordinate character), were then identified and optimised. The energy barriers between the different triplet states were confirmed to be small which makes all triplet states accessible. Solvent trapping, which occurs on the singlet PES according to Wigner's rules, is finally achieved by a singlet pentacoordinate species to yield the monosolvento photoproduct. Thus, our calculations not only reveal highly novel 3MC states but more significantly demonstrate their crucial role in the formation of the experimentally observed photoproducts.

Orbit-orbit relativistic correction calculated with all-electron molecular explicitly correlated Gaussians.

An algorithm for calculating the first-order electronic orbit-orbit magnetic interaction correction for an electronic wave function expanded in terms of all-electron explicitly correlated molecular Gaussian (ECG) functions with shifted centers is derived and implemented. The algorithm is tested in calculations concerning the H2 molecule. It is also applied in calculations for LiH and H3+ molecular systems. The implementation completes our work on the leading relativistic correction for ECGs and paves the way for very accurate ECG calculations of ground and excited potential energy surfaces (PESs) of small molecules with two and more nuclei and two and more electrons, such as HeH-, H3+, HeH2+, and LiH2+. The PESs will be used to determine rovibrational spectra of the systems.

Intramolecular Singlet Fission in Quinoidal Bi- and Tetrathiophenes: A Comparative Study of Low-Lying Excited Electronic States and Potential Energy Surfaces.

Quinoidal bithiophene has recently been introduced ( Varnavski, O. et al. J. Phys. Chem. Lett. 2015 , 6 , 1375 - 1384 ) as a very promising isolated organic compound for intramolecular singlet fission (iSF) with an outstanding SF quantum yield of ≈180%. In contrast, another recent study ( Ren, L. et al. J. Am. Chem. Soc. 2015 , 137 , 11294 - 11302 ) revealed that quinoidal tetrathiophenes have no activity in the iSF process and are strong fluorophores instead, with measured fluorescent quantum yields up to 53.1%. Using DFT and TD-DFT methods, the authors of the second contribution attributed the marked differences between these compounds to faster reverse T2 → S1 intersystem crossing processes in the tetrathiophenes. To address this unprecedented discrepancy, quinoidal bithiophene and tetrathiophene compounds and their derivatives are carefully examined using the CASPT2 technique. Theoretical evidence is provided through detailed investigation of CASPT2 potential energy surfaces of different singlet and triplet states involved in the iSF process. Through comparison of the CASPT2 results with the CASSCF and RAS-2SF data, it is found that the dynamic electron correlation present in the CASPT2 method plays a crucial role for correct description of the multiexciton nature of the triplet pair 1[TT] state in quinoidal bi- and tetrathiophenes. Effects of substitution and structural modification on iSF activity of these compounds are also examined using the CASPT2 method where the obtained results are in accordance with previous experimental predictions. These results contribute to a better understanding of the iSF mechanism in quinoidal systems which could be relevant for designing new iSF active compounds.

Long-lived coherence in pentafluorobenzene as a probe of ππ(*) - πσ(*) vibronic coupling.

The dynamics of pentafluorobenzene after femtosecond laser excitation to the optically bright ππ(*) first excited electronic state have been investigated by femtosecond time-resolved time-of-flight mass spectrometry and femtosecond time-resolved photoelectron imaging spectroscopy. The observed temporal profiles exhibit a bi-exponential decay behavior with a superimposed, long-lived, large-amplitude oscillation with a frequency of νosc = 78-74 cm(-1) and a damping time of τD = 5-2 ps. On the basis of electronic structure and quantum dynamics calculations, the oscillations have been shown to arise due to vibronic coupling between the optically bright ππ(*) state and the energetically close-lying optically dark πσ(*) state. The coupling leads to a pronounced double-well character of the lowest excited adiabatic potential energy surface along several out-of-plane modes of b1 symmetry. The optical electronic excitation initiates periodic wavepacket motion along these modes. In the out-of-plane distorted molecular configuration, the excited state acquires substantial πσ(*) character, thus modulating the ionization probability. The photoelectron spectra and the anisotropy of their angular distribution confirm the periodically changing electronic character. The ionizing probe laser pulse directly maps the coupled electron-nuclear motion into the observed signal oscillations.

Quantum wavepacket dynamics of the N([formula omitted]) + NO([formula omitted]) reaction and its isotopic variants: Integral cross sections and thermal rate constants

We investigate the initial state-selected dynamics of the title reaction on its ground (1 3A″) and first excited (1 3A′) triplet potential energy surfaces (PESs) by a time-dependent wavepacket propagation method, employing the ab initio analytical PESs developed by Gamallo et al. (2003). All partial wave contributions up to the total angular momentum J=140 are found to be necessary for the scattering of NO diatom in its vibrational and rotational ground state up to a collision energy ∼0.9eV. The converged initial state-selected reaction attributes viz., reaction probabilities, integral cross sections and thermal rate constants are obtained within the centrifugal sudden (CS) approximation and the convergence of the results are carefully checked by varying all parameters used in the numerical calculations. The dynamical results are compared with the other reported theoretical and experimental findings. Investigation on the energy-resolved channel-specific reaction probabilities infers that the N2 formation channel is very much favorable than the N-exchange channel. The reaction proceeds via some metastable resonances, observed from the oscillatory probability curves, which is more in the latter channel compared to the former. The effect of rotational and vibrational excitations of the reagent (NO diatom) on the dynamics is examined. We also examine the effect of isotopic substitution of N-atom (14N by 15N) on the reaction dynamics.

Control of Nonadiabatic Passage through a Conical Intersection by a Dynamic Resonance.

Nonadiabatic processes, dominated by dynamic passage of reactive fluxes through conical intersections (CIs), are considered to be appealing means for manipulating reaction paths, particularly via initial vibrational preparation. Nevertheless, obtaining direct experimental evidence of whether specific-mode excitation affects the passage at the CI is challenging, requiring well-resolved time- or frequency-domain experiments. Here promotion of methylamine-d2 (CH3ND2) molecules to spectral-resolved rovibronic states on the excited S1 potential energy surface, coupled to sensitive D photofragment probing, allowed us to follow the N-D bond fission dynamics. The branching ratios between slow and fast D photofragments and the internal energies of the CH3ND(X̃) photofragments confirm correlated anomalies for predissociation initiated from specific rovibronic states. These anomalies reflect the existence of a dynamic resonance that strongly depends on the energy of the initially excited rovibronic states, the evolving vibrational mode on the repulsive S1 part during N-D bond elongation, and the manipulated passage through the CI that leads to CH3ND radicals excited with C-N-D bending. This resonance plays an important role in the bifurcation dynamics at the CI and can be foreseen to exist in other photoinitiated processes and to control their outcome.

Luminescence of the (O2(a(1)Δ(g)))2 collisional complex in the temperature range of 90-315 K: Experiment and theory.

Experimental and theoretical studies of collision induced emission of singlet oxygen molecules O2(a(1)Δg) in the visible range have been performed. The rate constants, half-widths, and position of peaks for the emission bands of the (O2(a(1)Δg))2 collisional complex centered around 634 nm (2) and 703 nm (3) have been measured in the temperature range of 90-315 K using a flow-tube apparatus that utilized a gas-liquid chemical singlet oxygen generator. The absolute values of the spontaneous emission rate constants k2 and k3 are found to be similar, with the k3/k2 ratio monotonically decreasing from 1.1 at 300 K to 0.96 at 90 K. k2 slowly decreases with decreasing temperature but a sharp increase in its values is measured below 100 K. The experimental results were rationalized in terms of ab initio calculations of the ground and excited potential energy and transition dipole moment surfaces of singlet electronic states of the (O2)2 dimole, which were utilized to compute rate constants k2 and k3 within a statistical model. The best theoretical results reproduced experimental rate constants with the accuracy of under 40% and correctly described the observed temperature dependence. The main contribution to emission process (2), which does not involve vibrational excitation of O2 molecules at the ground electronic level, comes from the spin- and symmetry-allowed 1(1)Ag←(1)B3u transition in the rectangular H configuration of the dimole. Alternatively, emission process (3), in which one of the monomers becomes vibrationally excited in the ground electronic state, is found to be predominantly due to the vibronically allowed 1(1)Ag←2(1)Ag transition induced by the asymmetric O-O stretch vibration in the collisional complex. The strong vibronic coupling between nearly degenerate excited singlet states of the dimole makes the intensities of vibronically and symmetry-allowed transitions comparable and hence the rate constants k2 and k3 close to one another.

Calculating time-resolved differential absorbance spectra for ultrafast pump-probe experiments with surface hopping trajectories.

We report a surface hopping approach for modeling the full time- and frequency-resolved differential absorbance spectra (beyond the inhomogenous limit) obtained in ultrafast pump-probe experiments. In our approach, we combine dynamical information obtained from ensembles of classical trajectories propagated on the ground and on the excited potential energy surfaces to directly calculate optical response functions and hence spectral lineshapes. We demonstrate that our method is exact for the model problem of two shifted harmonic potentials with identical harmonic frequencies in the absence of electronic relaxation. We then consider a model three state system with electronic relaxation and show that our method is able to capture the effects of nonadiabatic excited state dynamics on the time-dependent differential absorbance spectra. Furthermore, by comparing our spectra against those spectra calculated with either an (1) inhomogenous expression, (2) ground-state Kubo theory, or (3) excited-state Kubo theory, we show that including dynamical information from both the ground and excited potential energy surfaces significantly improves the reliability of the semiclassical approximations. As such, our surface hopping method should find immediate use in modeling the time-dependent differential abosrbance spectra of ultrafast pump-probe experiments.

Ab initio study of the Ar–CS2(V1B2) intermolecular potential surface: effect of van der Waals interaction on the emission of CS2 molecule

In this work, the excited state intermolecular potential energy surface of the Ar–CS2(V1B2) van der Waals complex was evaluated for the first time. The calculation of more than 4000 single-point interaction energies for the complex using an equation-of-motion coupled-cluster model with single and double substitutions level of theory with extended basis set involving bond functions has been performed. After fitting the interaction energies to analytical functions, the emission spectra of the Ar–CS2(V1B2) complex related to the different stationary points on the potential energy surface were calculated. It was seen that the intensity and the position of the emission spectra are dependent on the orientation of the Ar atom around the bent excited CS2 and the distance between two components. The information about the structural parameters of the complex related to the global minimum was obtained under the pseudodiatomic approximation with assistance of ab initio potential. The presented investigation could be useful for further theoretical and experimental studies of Ar–CS2(V1B2) complex.

How to calculate linear absorption spectra with lifetime broadening using fewest switches surface hopping trajectories: a simple generalization of ground-state Kubo theory.

In this paper, we develop a surface hopping approach for calculating linear absorption spectra using ensembles of classical trajectories propagated on both the ground and excited potential energy surfaces. We demonstrate that our method allows the dipole-dipole correlation function to be determined exactly for the model problem of two shifted, uncoupled harmonic potentials with the same harmonic frequency. For systems where nonadiabatic dynamics and electronic relaxation are present, preliminary results show that our method produces spectra in better agreement with the results of exact quantum dynamics calculations than spectra obtained using the standard ground-state Kubo formalism. As such, our proposed surface hopping approach should find immediate use for modeling condensed phase spectra, especially for expensive calculations using ab initio potential energy surfaces.

TDDFT modeling of the CO‐photolysis of Fe2(S2C3H6)(CO)6, a model of the [FeFe]‐hydrogenase catalytic site

Upon irradiation with ultraviolet wavelengths, Fe2(S2C3H6)(CO)6, a simple model of the [FeFe]‐hydrogenase active site, undergoes CO dissociation to form the unsaturated Fe2(S2C3H6)(CO)5 species and successively a solvent adduct at the vacant coordination site. In the present work, the CO‐photolysis of Fe2(S2C3H6)(CO)6 was investigated by density functional theory (DFT) and time‐dependent DFT (TDDFT). Trans Fe2(S2C3H6)(CO)5 form and the corresponding trans heptane or acetonitrile solvent adducts are the lowest energy ground state forms. CO dissociation barriers computed for the lowest triplet state are roughly halved with respect to those for the ground state suggesting that some low‐lying excited potential energy surface (PES) could be loosely bound with respect to FeC bond cleavage. The TDDFT excited state PESs and geometry optimizations for the excited states likely involved in the CO‐photolysis suggest that the FeS bond elongation and the partial isomerization toward the rotated form could take place simultaneously, favoring the trans CO photodissociation. © 2014 Wiley Periodicals, Inc.

Using Ion-velocity Map Imaging Technique to Study Photodissociation of 2-Bromopentane

The photodissociation dynamics of 2-bromopentane at ∼234 nm has been investigated by utilizing ion-velocity map imaging technique. The mapped images of Br(2P3/2) (denoted as Br) and Br(2P1/2) (denoted as Br*) fragments were analyzed by means of the speed and angular distributions, respectively. The speed distributions can be fitted with two Gaussian components which are correlated to the two independent reaction paths on the excited potential energy surfaces (PES). The high-energy component is from the prompt dissociation along the C—Br stretching mode, while the low-energy one is related to the dissociation from the coupling of the C—Br stretching and bending modes. Relative quantum yield is measured to be 0.892 for Br in the photodissociation of 2-bromopentane at 234 nm. Combining the anisotropy parameter with the relative quantum yield of Br and Br* fragments, the contributions of the excited 3Q0, 3Q1, and 1Q1 states to the products Br and Br* were derived. The effect of alkyl branching on the mechanism of photodissociation was discussed by comparing the photodissociation processes of four isomers of bromopentane.

Assessment of Density Functional Theory for Describing the Correlation Effects on the Ground and Excited State Potential Energy Surfaces of a Retinal Chromophore Model.

In the quest for a cost-effective level of theory able to describe a large portion of the ground and excited potential energy surfaces of large chromophores, promising approaches are rooted in various approximations to the exact density functional theory (DFT). In the present work, we investigate how generalized Kohn-Sham DFT (GKS-DFT), time-dependent DFT (TDDFT), and spin-restricted ensemble-DFT (REKS) methods perform along three important paths characterizing a model retinal chromophore (the penta-2,4-dieniminium cation) in a region of near-degeneracy (close to a conical intersection) with respect to reference high-level multiconfigurational wave function methods. If GKS-DFT correctly describes the closed-shell charge transfer state, only TDDFT and REKS approaches give access to the open-shell diradical, one which sometimes corresponds to the electronic ground state. It is demonstrated that the main drawback of the usual DFT-based methods lies in the absence of interactions between the charge transfer and the diradicaloid configurations. Hence, we test a new computational scheme based on the State-averaged REKS (SA-REKS) approach, which explicitly includes these interactions into account. The State-Interaction SA-REKS (SI-SA-REKS) method significantly improves on the REKS and the SA-REKS results for the target system. The similarities and differences between DFT and wave function-based approaches are analyzed according to (1) the active space dimensions of the wave function-based methods and (2) the relative electronegativities of the allyl and protonated Schiff base moieties.