Theoretical study of the electronic nonadiabatic transitions in the photoelectron spectroscopy of F2O

The photoelectron spectrum of F2O pertaining to ionizations to the ground (X2B1) and low-lying excited electronic states (A2B2, B2A1, and C2A2) of F2O+ is investigated theoretically. The near equilibrium potential energy surfaces of the ground electronic state (X2B1) of F2O and the mentioned ground and excited electronic states of F2O+ reported by Wang et al. ( J. Chem. Phys. 2001, 114, 10682) for the C2v configuration are extended for the Cs geometry assuming a harmonic vibration along the asymmetric stretching mode. The vibronic interactions between the A2B2 and B2A1 electronic states of F2O+ are treated within a linear coupling approach, and the strength of the vibronic coupling parameter is calculated by an ab initio method. The nuclear dynamics is simulated by both time-independent quantum mechanical and time-dependent wave packet approaches. Although the first photoelectron band exhibits resolved vibrational progression along the symmetric stretching mode, the second one is highly overlapping. The latter is attributed to the nonadiabatic interactions among the energetically close A2B2, B2A1, and C2A2 electronic states of F2O+. The theoretical findings are in good accord with the available experimental results.     

Ab initio quantum dynamical study of photoinduced ring opening in furan

The nonadiabatic photoinduced ring opening occurring in the two lowest excited singlet states of furan is investigated theoretically, using wave-packet propagation techniques. The underlying multidimensional potential energy surfaces (PESs) are obtained from ab initio computations, using the equation-of-motion coupled cluster method restricted to single and double excitations (EOM-CCSD), reported in earlier recent work [E. V. Gromov, A. B. Trofimov, F. Gatti, and H. Ko?ppel, J. Chem. Phys. 133, 164309 (2010)]. Up to five nuclear degrees of freedom are considered in the quantum dynamical treatment. Four of them represent in-plane motion for which the electronic states in question (correlating with the valence (1)B(2)(V) and Rydberg (1)A(2)(3s) states at the C(2v) ground-state molecular configuration) have different symmetries, A(') and A('), respectively. The fifth mode, representing out-of-plane bending of the oxygen atom against the carbon-atom plane, leads to an interaction of these states, as is crucial for the photoreaction. The nonadiabatic coupling and conical intersection cause an electronic population transfer on the order of ～10 fs. Its main features, and that of the wave-packet motion, are interpreted in terms of properties of the PES. The lifetime due to the ring-opening process has been estimated to be around 2 ps. The dependence of this estimate on the nuclear degrees of freedom retained in the computations is discussed.     

Communication: multistate quantum dynamics of photodissociation of carbon dioxide between 120 nm and 160 nm

UV absorption cross section of CO(2) is studied using high level ab initio quantum chemistry for electrons and iterative quantum dynamics for nuclear motion on interacting global full dimensional potential energy surfaces. Six electronic states-1, 2, 3(1)A(') and 1, 2, 3(1)A(")-are considered. At linearity, they correspond to the ground electronic state X?(1)Σ(g) (+) and the optically forbidden but vibronically allowed valence states 1(1)Δ(u), 1(1)Σ(u) (-), and 1(1)Π(g). In the Franck-Condon region, these states interact via Renner-Teller and conical intersections and are simultaneously involved in an intricate network of non-adiabatic couplings. The absorption spectrum, calculated for many rotational states, reproduces the distinct two-band shape of the experimental spectrum measured at 190 K and the characteristic patterns of the diffuse structures in each band. Quantum dynamics unravel the relative importance of different vibronic mechanisms, while metastable resonance states, underlying the diffuse structures, provide dynamically based vibronic assignments of individual lines.     

A dispersed fluorescence and ab initio investigation of the X2B1 and A2A1 electronic states of the PH2 molecule

In this work, the X2B1 and A2A1 electronic states of the phosphino (PH2) free radical have been studied by dispersed fluorescence and ab initio methods. PH2 molecules were produced in a molecular free-jet apparatus by laser vaporizing a silicon rod in the presence of phosphine (PH3) gas diluted in helium. The laser-induced fluorescence, from the excited A2A1 electronic state down to the ground electronic state, was dispersed and analyzed. Ten (upsilon1upsilon2upsilon3) vibrationally excited levels of the ground electronic state, with upsilon1 < or = 2, upsilon2 < or = 6, and upsilon3 = 0, have been observed. Ab initio potential-energy surfaces for the X2B1 and A2A1 electronic states have been calculated at 210 points. These two states correlate with a 2Pi(u) state at linearity and they interact by the Renner-Teller coupling and spin-orbit coupling. Using the ab initio potential-energy surfaces with our RENNER computer program system, the vibronic structure and relative intensities of the A2A1 --> X2B1 emission band system have been calculated in order to corroborate the experimental assignments.     

On the (Emultiply sign in circlee)-Jahn-Teller conical intersections in the 3p(E') and 3d(E") Rydberg electronic states of triatomic hydrogen

The static and dynamic aspects of the Jahn-Teller (JT) interactions in the 3p(E') and 3d(E") Rydberg electronic states of H3 are analyzed theoretically. The static aspects are discussed based on recent ab initio quantum chemistry results, and the dynamic aspects are examined in terms of the vibronic spectra and nonradiative decay behavior of these states. The adiabatic potential-energy surfaces of these degenerate electronic states are derived from extensive ab initio calculations. The calculated adiabatic potential-energy surfaces are diabatized following our earlier study on this system in its 2p(E') ground electronic state. The nuclear dynamics on the resulting conically intersecting manifold of electronic states is studied by a time-dependent wave-packet approach. Calculations are performed both for the uncoupled and coupled state situations in order to understand the importance of nonadiabatic interactions due to the JT conical intersections in these excited Rydberg electronic states.     

Theoretical study of photoinduced ring-opening in furan

The potential energy surfaces (PESs) of the two lowest excited singlet states of furan [correlating with the Rydberg (1)A(2)(3s) and valence (1)B(2)(V) states at the C(2v) ground-state molecular configuration] have been studied in some detail with regard to the photoinduced ring-opening reaction. The surfaces have been characterized in terms of their stationary points and points of minimum energy conical intersections along the ring-opening pathway. The optimization of the geometrical parameters has been performed with the equation of motion coupled cluster singles and doubles method. The ab initio PESs have been modeled by energy grids and Taylor series. The resulting 11-dimensional PESs reproduce the ab initio results to a good accuracy and can be used in dynamical calculations.     

Nonadiabatic coupling and diabatic electronic population dynamics on 11A2 and 11B1 states of ozone molecule

In this work, we examine nonadiabatic population dynamics for 1¹B₁ and 1¹A₂ states of ozone molecule (O₃). In O₃, two lowest singlet excited states, ¹A₂ and ¹B₁, can be coupled. Thus, population transfer between them occurs through the seam involving these two states. At any point of the seam (conical intersection), the Born-Oppenheimer approximation breaks down, and it is necessary to investigate nonadiabatic dynamics. We consider a linear vibronic coupling Hamiltonian model and evaluate vibronic coupling constant, diabatic frequencies for three modes of O₃, bilinear and quadratic coupling constants for diabatic potentials, displacements, and Huang-Rhys coupling constants using ab initio calculations. The electronic structure calculations have been performed at the multireference configuration interaction and complete active space with second-order perturbation theory with a full-valence complete active space self-consistent field methods and augmented Dunning's standard correlation-consistent-polarized quadruple zeta basis set to determine ab initio potential energy surfaces for the ground state and first two excited states of O₃, respectively. We have chosen active space comprising 18 electrons distributed over 12 active orbitals. Our calculations predict the linear vibronic coupling constant 0.123 eV. We have obtained the population on the 1¹B₁ and 1¹A₂ excited electronic states for the first 500 fs after photoexcitation.     

On the simulation of photoelectron spectra in molecules with conical intersections and spin-orbit coupling: the vibronic spectrum of CH3S

A method to simulate photoelectron spectra for states coupled by conical intersections and the spin-orbit interaction is reported. The algorithm is based on the multimode vibronic coupling model and treats the spin-orbit interaction in a nonperturbative manner. Since the algorithm is not dependent on molecular symmetry, the approach is generally applicable to accidental conical intersections as well as the symmetry required intersections found in Jahn-Teller molecules. The method is also computationally efficient using energy gradient and derivative coupling information to limit the number of nuclear configurations at which ab initio data are required. This approach is applied to simulate the negative ion photoelectron spectrum of the methylthio radical. The two-state Hamiltonian employed to describe this system was determined employing ab initio gradients and derivative couplings at only 17 nuclear configurations.     

Potential-energy surface, dynamics of van der Waals motions, and vibronic transitions in p-difluorobenzene-argon complex

The dynamics of van der Waals vibrational motions and vibronic spectrum of the complex of argon with p-difluorobenzene (ArDFB) are investigated using the ab initio method. The electronic ground-state potential-energy surface of the complex is calculated at the second-order M?ller-Plesset level of theory using a well-balanced basis set aug-cc-pVDZ and its reduced version without tight polarization functions. The dissociation energy of 351 cm(-1) and the binding energy of 402 cm(-1) determined at the Ar distance of 3.521 Angstroms from the DFB ring well agree with the experimental data available. The character of calculated vibrational levels is analyzed and the effect of a strong coupling between the stretching and bending motions is investigated. A new class of hybrid states created by this coupling is found. To investigate the vibronic S(1)-S(0) spectrum, the surfaces of the electronic transition dipole moment are calculated using the ab initio method. From these surfaces, the vibronic transition intensities are determined and employed to assign the Franck-Condon- and Herzberg-Teller-induced transitions.     

Fluorescence and REMPI spectroscopy of jet-cooled isolated 2-phenylindene in the S1 state

We investigated the spectroscopy of the first excited singlet electronic state S1 of 2-phenylindene using both fluorescence excitation spectroscopy and resonantly enhanced multiphoton ionization spectroscopy. Moreover, we investigated the dynamics of the S1 state by determining state-selective fluorescence lifetimes up to an excess energy of approximately 3400 cm(-1). Ab initio calculations were performed on the torsional potential energy curve and the equilibrium and transition state geometries and normal-mode frequencies of the first excited singlet state S1 on the CIS level of theory. Numerous vibronic transitions were assigned, especially those involving the torsional normal mode. The torsional potentials of the ground and first excited electronic states were simulated by matching the observed and calculated torsional frequency spacings in a least-squares fitting procedure. The simulated S1 potential showed very good agreement with the ab initio potential calculated on the CIS/6-31G(d,p) level of theory. TDDFT energy corrections improved the match with the simulated S(1) torsional potential. The latter calculation yielded a torsional barrier of V2 = 6708 cm(-1), and the simulation a barrier of V2 = 6245 cm(-1). Ground-state normal-mode frequencies were calculated on the B3LYP/6-31G(d,p) level of theory, which were used to interpret the infrared spectrum, the FDS spectrum of the transition and hot bands of the FES spectrum. The fluorescence intensities of the nu49 overtone progression could reasonably be reproduced by considering the geometry changes upon electronic excitation predicted by the ab initio calculations. On the basis of the torsional potential calculations, it could be ruled out that the uniform excess energy dependence of the fluorescence lifetimes is linked to the torsional barrier in the excited state. The rotational band contour simulation of the transition yielded rotational constants in close agreement to the ab initio values for both electronic states. Rotational coherence signals were obtained by polarization-analyzed, time-resolved measurements of the fluorescence decay of the transition. The simulation of these signals yielded corroborating evidence as to the quality of the ab initio calculated rotational constants of both states. The origin of the anomalous intensity discrepancy between the fluorescence excitation spectrum and the REMPI spectrum is discussed.     

Combined experimental-theoretical study of the lower excited singlet states of paravinyl phenol, an analog of the paracoumaric acid chromophore

The low-lying excited singlet states of paravinyl phenol (pVP) are investigated experimentally and theoretically paying attention to their similarity to excited states of paracoumaric acid, the chromophore of the photoactive yellow protein (PYP). Resonance enhanced multiphoton ionization and laser induced fluorescence spectroscopic techniques are employed to obtain supersonically cooled, vibrationally resolved excitation and emission spectra related to the lowest (1)A'(V') excited state of pVP. Comprehensive analyses of the spectral structures are carried out by means of the equation-of-motion coupled cluster singles and doubles and time dependent density functional theory methods in combination with the linear vibronic coupling model and Franck-Condon calculations. The assignments of the spectral patterns are given, mostly in terms of excitations of totally symmetric modes. Weak activity of the non-totally-symmetric modes indicates low probability of photochemical processes in the Franck-Condon region of the (1)A'(V') state. The second (1)A'(V) and third (1)A" (Ryd) excited states of pVP are characterized with regard to their electronic structure, properties, and effects of geometry relaxations. The lengthening of the double bond relevant to the trans-cis isomerization of the PYP chromophore is found for the (1)A'(V) state. A possibility of photochemical processes and strong vibronic interactions in this state can be expected. The theoretical results for the (1)A"(Ryd) state predict that dissociation with respect to the O-H bond is possible.     

Ab initio molecular dynamics of excited-state intramolecular proton transfer around a three-state conical intersection in malonaldehyde

Excited-state potential energy surface (PES) characterization is carried out at the CASSCF and MRSDCI levels, followed by ab initio dynamics simulation of excited-state intramolecular proton transfer (ESIPT) on the S2(pipi*) state in malonaldehyde. The proton-transfer transition state lies close to an S2/S1 conical intersection, leading to substantial coupling of proton transfer with electronic relaxation. Proton exchange proceeds freely on S2, but its duration is limited by competition with twisting out of the molecular plane. This rotamerization pathway leads to an intersection of the three lowest singlet states, providing the first detailed report of ab initio dynamics around a three-state intersection (3SI). There is a significant energy barrier to ESIPT on S1, and further pyramidalization of the twisted structure leads to the minimal energy S1/S0 intersection and energetic terminal point of excited-state dynamics. Kinetics and additional mechanistic details of these pathways are discussed. Significant depletion of the spectroscopic state and recovery of the ground state is seen within the first 250 fs after photoexcitation.     

On the vibronic coupling approximation: a generally applicable approach for determining fully quadratic quasidiabatic coupled electronic state Hamiltonians

In this report we introduce an iterative procedure for constructing a quasidiabatic Hamiltonian representing N(state)-coupled electronic states in the vicinity of an arbitrary point in N(int)-dimensional nuclear coordinate space. The Hamiltonian, which is designed to compute vibronic spectra employing the multimode vibronic coupling approximation, includes all linear terms which are determined exactly using analytic gradient techniques. In addition, all [N(state)][N(int)] quadratic terms, where [n]=n(n+1)/2, are determined from energy gradient and derivative coupling information obtained from reliable multireference configuration interaction wave functions. The use of energy gradient and derivative coupling information enables the large number of second order parameters to be determined employing ab initio data computed at a limited number of points (N(int) being minimal) and assures a maximal degree of quasidiabaticity. Numerical examples are given in which quasidiabatic Hamiltonians centered around three points on the C(3)H(3)N(2) potential energy surface (the minimum energy point on the ground state surface and the minimum energy points on the two- and three-state seams of conical intersection) were computed and compared. A method to modify the conical intersection based Hamiltonians to better describe the region of the ground state minimum is introduced, yielding improved agreement with ab initio results, particularly in the case of the Hamiltonian defined at the two-state minimum energy crossing.     

Vibronic coupling and double excitations in linear response time-dependent density functional calculations: dipole-allowed states of N2

The present study serves two purposes. First, we evaluate the ability of present time-dependent density functional response theory (TDDFRT) methods to deal with avoided crossings, i.e., vibronic coupling effects. In the second place, taking the vibronic coupling effects into account enables us, by comparison to the configuration analysis in a recent ab initio study [J. Chem. Phys. 115, 6438 (2001)], to identify the neglect of double excitations as the prime cause of limited accuracy of these linear response based TDDFRT calculations for specific states. The "statistical averaging of (model) orbital potentials (SAOP)" Kohn-Sham potential is used together with the standard adiabatic local-density approximation (ALDA) for the exchange-correlation kernel. We use the N2 molecule as prototype, since the TDDFRT/SAOP calculations have already been shown to be accurate for the vertical excitations, while this molecule has a well-studied, intricate vibronic structure as well as significant double excitation nature in the lowest 1Pi(u) state at elongated bond lengths. A simple diabatizing scheme is employed to obtain a diabatic potential energy matrix, from which we obtain the absorption spectrum of N2 including vibronic coupling effects. Considering the six lowest dipole allowed transitions of 1Sigma(u)+ and 1Pi(u) symmetry, we observe a good general agreement and conclude that avoided crossings and vibronic coupling can indeed be treated satisfactorily on the basis of TDDFRT excitation energies. However, there is one state for which the accuracy of TDDFRT/ALDA clearly breaks down. This is the state for which the ab initio calculations find significant double excitation character. To deal with double excitation character is an important challenge for time-dependent density functional theory.     

Calculation of the vibronic structure of the photodetachment spectra of CCCl- and CCBr-

The vibronic structure of the closely spaced and strongly coupled X 2Sigma+ and A 2Pi states in the photodetachment spectra of CCCl- and CCBr- has been calculated by considering Sigma-Pi vibronic coupling together with spin-orbit coupling. The stretching modes are treated within the so-called linear-vibronic-coupling model. The vibronic and spin-orbit parameters have been determined by accurate ab initio electronic-structure calculations. While the nonrelativistic vibronic-coupling parameters are of approximately equal strength in CCCl and CCBr, the vibronic-coupling parameters of spin-orbit origin are found to be larger in the latter. The calculated photodetachment spectra of both systems are shown to exhibit a complicated vibronic structure due to strong Sigma-Pi vibronic coupling. The spectral envelopes of the calculated photodetachment spectra exhibit a double-hump reminiscent of strongly coupled Exe Jahn-Teller systems.     

Vibronic coupling in the excited cationic states of ethylene: simulation of the photoelectron spectrum between 12 and 18 eV

The effect of vibronic coupling on structure and spectroscopy is investigated in the excited cationic states of ethylene. It is found from equation of motion coupled cluster singles and doubles method for ionization potential electronic structure calculations in a triple-zeta plus double polarization basis set that ethylene in its third (B (2)A(g)) and fourth (C (2)B(2u)) ionized states does not have a stable minimum-energy geometry. The potential-energy surfaces of these states are energetically distinct and well separated at the ground-state geometry of ethylene, but in a geometry optimization as the structure of the ion relaxes, these surfaces end up in conical intersections and finally in the stable equilibrium geometry of the second ionized state (A (2)B(3g)). The topology of the potential-energy surfaces can be clearly understood using a vibronic model Hamiltonian. Furthermore, by diagonalizing this model Hamiltonian, the photoelectron spectrum of ethylene corresponding to the second, third, and fourth ionized states (12-18 eV) is simulated. Spectra from vibronic simulations including up to quartic coupling constants and using various normal-mode basis sets are compared to those from vertical Franck-Condon simulations to understand the importance of vibronic coupling and nonadiabatic effects and to examine the influence of individual normal modes on the spectrum.     

Adiabatic versus diabatic descriptions of the lowest Rydberg and valence 1Σ+ states of HCl

In this contribution we first report new ab initio self-consistent field configuration interaction calculations of the first excited adiabatic potential of (1)Σ(+) symmetry, the 2(1)Σ(+) or B(1)Σ(+) state, which presents two minima and can thus be seen as made up of the Rydberg E(1)Σ(+) and the valence V(1)Σ(+) states. Based on the computed 2(1)Σ(+) potential, we devised a theoretical procedure to compute the vibronic structure in order to try to explain the energy levels observed in the region above 76 254.4 cm(-1) which display an irregular vibrational structure, indicative of spectral perturbations. We try to find out which representation of the electronic states, the diabatic or the adiabatic one, is best suited to replicate the lowest observed vibronic levels of the E and V states. To this end, we deduce, from the 2(1)Σ(+) potential and its complementary adiabatic potential, two diabatic potentials. We then carry out a coupled equation treatment based on these diabatic potentials. The results of this treatment indicate that, in the present case, the adiabatic representation is better than the diabatic one to describe the observed vibronic levels. This is due, as expected, to the existence of a strong electrostatic interaction between the two diabatic potentials.     

Strong vibronic coupling effects in ionization spectra: The “mystery band” of butatriene

A theory of vibronic coupling in molecules is presented and applied to butatriene. The energies and coupling constants which enter the calculation are computed using ab initio Hartree—Fock and many-body methods. The influence of the energy splitting and the coupling constants on the calculated spectrum is discussed. It is definitely shown that the “mystery band” in the photoelectron spectrum of butatriene arises from the vibronic coupling between the electronic states ²B_3g and ²B_3u. To reproduce the experimental observations it is essential to include in the calculation both totally and non-totally symmetric vibrational modes.     

Laser-induced fluorescence and pure rotational spectroscopy of the CH2CHS (vinylthio) radical

Laser-induced fluorescence (LIF) excitation spectra of the B-X (2)A(") electronic transition of the CH(2)CHS radical, which is the sulfur analog of the vinoxy (CH(2)CHO) radical, were observed under room temperature and jet-cooled conditions. The LIF excitation spectra show very poor vibronic structures, since the fluorescence quantum yields of the upper vibronic levels are too small to detect fluorescence, except for the vibrationless level in the B state. A dispersed fluorescence spectrum of jet-cooled CH(2)CHS from the vibrationless level of the B state was also observed, and vibrational frequencies in the X state were determined. Precise rotational and spin-rotation constants in the ground vibronic level of the radical were determined from pure rotational spectroscopy using a Fourier-transform microwave (FTMW) spectrometer and a FTMW-millimeter wave double-resonance technique [Y. Sumiyoshi et al., J. Chem. Phys. 123, 054324 (2005)]. The rotationally resolved LIF excitation spectrum for the vibronic origin band of the jet-cooled CH(2)CHS radical was analyzed using the ground state molecular constants determined from pure rotational spectroscopy. Determined molecular constants for the upper and lower electronic states agree well with results of ab initio calculations.