Coupled Potential Energy Research Articles

Direct diabatization of electronic states by the fourfold way. II. Dynamical correlation and rearrangement processes

Diabatic representation of coupled potential energy surfaces and their scalar couplings provides a compact and convenient starting point for dynamics calculations carried out in either the adiabatic or diabatic representation. In a previous paper we presented a general, path-independent scheme, called the fourfold way, for calculating diabatic surfaces and their scalar couplings from adiabatic surfaces and electronic density matrices such that the manifold of diabatic states spans the variationally optimized space of a finite number of adiabatic states. In the present paper we extend that scheme in these ways: (1) We show how to include dynamical electronic correlation energy by multireference perturbation theory or configuration interaction based on a complete active reference space. (2) We present a more general strategy for treating rearrangements. (3) We present consistency criteria for testing the validity of the assumptions for a particular choice of reference geometries, diabatic molecular orbital (DMO) ordering, dominant configuration-state-function lists, and choice(s) for reference DMO(s) for systems involving rearrangements. The first extension is illustrated by multiconfiguration quasidegenerate perturbation theory (MC-QDPT) calculations on LiF, and all three extensions are illustrated by MC-QDPT calculations on the reaction Li(2 2S,2 2P)+HF→LiF+H.

Clusters containing open-shell molecules. III. Quantum five-dimensional/two-surface bound-state calculations on ArnOH van der Waals clusters (X2Π, n=4 to 12)

This paper presents a theoretical study of the bound states of the open-shell OH radical in its ground electronic state (X2Π) interacting with n Ar atoms, for n from 4 to 12. After freezing the geometry of the Arn cage or subunit at the equilibrium structure (preceding paper), we carry out nonadiabatic five-dimensional quantum dynamics calculations on two coupled potential energy surfaces, using an extension of the method previously applied to closed-shell ArnHF clusters [J. Chem. Phys. 103, 1829 (1995)]. The method is based on a discrete variable representation (DVR) for the translational motion of OH relative to Arn, combined with a finite basis representation of the OH hindered rotation and electronic structure, including spin–orbit effects. The pattern of OH hindered rotor levels in clusters is similar to that in Ar–OH itself, though extended over three to four times the energy range for n=4 to 9. Ar12OH has a nearly spherical shell of Ar atoms around the OH, so the anisotropic splitting is very small. For n=10 and 11, the anisotropy may be viewed as arising from holes in an otherwise spherical shell, and the resulting patterns of hindered rotor levels are inverted versions of those for Ar2OH and Ar–OH.

Near-dissociation states and coupled potential curves for the HeN+ complex

The near-dissociation microwave rovibronic spectra of HeN+ [Carrington et al., Chem. Phys. Lett. 262, 598 (1996)] are used to obtain coupled potential energy curves for the six electronic states correlating with He+N+ 3P0, 3P1, and 3P2. High-quality ab initio calculations are carried out, using a spin-restricted open-shell coupled-cluster method with an augmented correlation-consistent quintuple-zeta basis set (aug-cc-pV5Z). Fully coupled calculations of bound and quasibound states are performed, including all six electronic states, and suggest two possible assignments of the observed transitions. The potentials are then morphed (scaled) to reproduce the experimental frequencies. One of the two assignments, designated SH1, is preferred because it gives a more satisfactory explanation of the observed hyperfine splittings. The corresponding morphed potential has well depths of 1954 cm−1 and 192 cm−1 for the spin-free 3Σ− and 3Π curves, respectively.

Multistate vibronic interactions in the benzene radical cation. I. Electronic structure calculations

The multistate vibronic interactions in the benzene radical cation are investigated theoretically, employing the framework of a linear vibronic coupling scheme. The five lowest electronic states are included in the treatment; in view of the degeneracy of some states, this amounts to eight coupled potential energy surfaces. Different types of ab initio calculations have been performed for the system parameters and been found to be in good mutual agreement, thus supporting each other. The calculations reveal a whole sequence of low-energy conical intersections between the potential energy surfaces of different states. Their importance for the nuclear dynamics in this prototypical organic radical cation is pointed out. Wave-packet dynamical simulations for these coupled potential energy surfaces will be presented in the following paper (Paper II).

Coupled quasidiabatic potential energy surfaces for LiFH

We present high-level ab initio calculations for the global adiabatic potential energy surfaces of the ground state (X̃ 2A′) and several excited states (Ã 2A′, B̃ 2A″, C̃ 2A′, D̃ 2A′, and Ẽ 2A″) of LiFH, including the valleys leading to Li+HF and LiF+H. The ab initio calculations were carried out using the multireference singles and doubles configuration interaction method with 99 reference configuration state functions (CSFs) for the A′2 states and 39 reference CSFs for the A″2 states. The basis set consisted of 140 contracted Gaussian functions, including specifically optimized diffuse functions, and calculations were performed on a dense grid of ∼3500 nuclear geometries which allowed us to construct an accurate analytic representation of the two lowest-energy LiFH potential energy surfaces. An analytic 2×2 quasidiabatic potential energy matrix was obtained by fitting physically motivated functional forms to the ab initio data for the two lowest-energy adiabatic states and explicitly including long-range interactions. The newly presented LiFH fit is compared to several ground-state LiFH fits and one excited-state LiFH fit that have appeared in the literature.

Charge transfer mechanism in N4+ + He and B3+ + He/H2 ion–atom/molecule collisions

AbstractAb initio potential energy curves and coupling matrix elements of the molecular states involved in the collision of the N4+(2s)2S and B3+(1s2)1S multicharged ions on the helium atom or molecular hydrogen have been determined by means of configuration interaction methods. The total and partial electron capture cross‐sections have been evaluated in the frame of a semiclassic approach in the 1‐ to 100‐keV laboratory energy range and compared to experimental data. A comparative study of both targets is performed in the case of the B3+ ion. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002

Photodissociation of LiFH and NaFH van der Waals complexes: A semiclassical trajectory study

The photodissociation of Li⋯FH and Na⋯FH van der Waals complexes is studied using Tully’s fewest-switches surface-hopping and the natural decay of mixing semiclassical trajectory methods for coupled-state dynamics. The lifetimes of the predissociated excited-state complex (exciplex), as well as the branching ratio into reactive and nonreactive arrangements and the internal energy distribution of the products are reported at several excitation energies. The semiclassical trajectory methods agree with each other only qualitatively, and the results are strongly dependent on the choice of electronic representation. In general, the lifetime of the LiFH exciplex is shorter and less dependent on the excitation energy than the lifetime of the NaFH exciplex. The semiclassical dynamics of LiFH and NaFH are interpreted in terms of the features of their coupled potential energy surfaces.

Interference dips in the single-crystal absorption spectrum of the ti-mu-fluoro-bis(trifluorochromate(III)) complex.

The lowest energy spin-allowed crystal field band of (Et(4)N)(3)Cr(2)F(9) shows a distinct interference dip at 15,000 cm(-1) with an approximate width of 200 cm(-1). This spectroscopic feature is due to spin-orbit coupling between the (2)E and (4)T(2) excited states and is analyzed with a set of two coupled potential energy surfaces. The minimum of the (4)T(2) potential surface is displaced along at least two normal coordinates. The modes involved cannot be directly determined from the unresolved absorption spectrum, but are obtained from Raman spectra and from the well-resolved spin-forbidden crystal field transition to the (2)A(1) state. The first mode with a frequency of 415 cm(-1) has predominant Cr-F stretching character; the second mode has a frequency of 90 cm(-1) and involves the entire Cr(2)F(9)(3-) dimer.

Semiclassical simulations of azomethane photochemistry in the gas phase and in solution.

We present semiclassical simulations of the dynamical events which follow the n --> pi excitation of an azomethane molecule: decay to the ground state, isomerization, and dissociation. Ab initio potential energy surfaces and couplings, slightly modified according to available experimental data, are employed in conjunction with a trajectory-surface-hopping method. For an isolated molecule, we show that dissociation takes place in the ground state, because the radiationless decay is very fast. The dissociation is mainly sequential: the methyldiazenyl radical first produced fragmentates very rapidly to N(2) + CH(3)*. The results of previous experiments by Lee's and Zewail's groups, from which partially conflicting conclusions had been drawn, are reproduced and interpreted. Molecular dynamics, coupled to the surface-hopping algorithm, allows us to simulate the photochemistry in acqueous solution. Here the fragmentation is suppressed because of vibrational energy loss to the solvent: only the isomerization takes place.

An Eikonal Treatment of Electronically Diabatic Photodissociation: Branching Ratios of CH3I

Collision-induced and photoinduced electronically diabatic transitions in polyatomic systems are described, starting with an eikonal representation of the molecular wave function and developing a self-consistent eikonal approximation for short deBroglie wavelengths. The approach provides state-to-state transition amplitudes for electronic excitation without requiring any preliminary knowledge of the nature of transitions between potential energy surfaces. The formalism has some similarities to recent semiclassical treatments using the initial value representation. It has been applied to the electronically diabatic dissociation CH3I + φ → CH3 + I induced by absorption of UV light using previously introduced potential energy surfaces and couplings to compare with accurate quantal results. Results for the model are given for branching ratios in the formation of I and I*, and for the final distribution of vibrational states of CH3 for two light wavelengths.

Coupled cluster ab initio potential energy surfaces for CO . . . He and CO . . .H 2

Ab initio potential energy surfaces including the vibrational coordinate dependence are presented for CO… He and CO… H2 using the coupled cluster method with Brueckner orbitals. The interaction energy is calculated using the supermolecule approach. The calculation of rate constants for the vibrational relaxation of CO(v = 1) by He and their comparison with the experimentally measured values over the temperature range 40–300 K is used to test the accuracy of the CO… He surface. Comparison with results from an earlier surface calculated by symmetry adapted perturbation theory shows that the two surfaces have similar scattering characteristics and reproduce the experimental measurements to a similar level of accuracy. The potential surface for the CO… H2 system is presented as raw data in anticipation of future calculations.

Coupled ab initio potential energy surfaces for the two lowest 2A′ electronic states of the C2H molecule

Realistic two-valued potential energy surfaces for the reaction C(3P) + CH(X2Π) → C2 + H have been constructed from a set of high level ab initio data describing the first two 2A′ electronic states of the C2H system. These states have linear equilibrium configurations, known as the X 2Σ+ and A2Π states, and are coupled by a conical intersection. They lead to the formation of C2(X1Σ+ g) and C2(a3Πu) considering an adiabatic dissociation process. The ab initio calculations are of the multireference configuration interaction variety and were carried out using a polarized triple-zeta basis set. Using the ab initio adiabatic energies and the matrix elements of the dipole moment, a 2 × 2 diabatic representation of the electronic Hamiltonian was built. Each element of this Hamiltonian matrix was expressed within the double many-body expansion (DMBE) scheme which is based, in this case, on the extended Hartree-Fock approximate correlation energy model (EHFACE). The analytical adiabatic potential energy surfaces are then obtained as the eigenvalues of this matrix, and display correctly the Σ/Π conical intersection. Moreover, the non-adiabatic couplings given by our analytical model are compared with the ab initio ones, and good qualitative agreement is observed.

Coupled ab initio potential energy surfaces for the two lowest 2 A' electronic states of the C 2 H molecule

Coupled ab initio potential energy surfaces for the two lowest 2 A' electronic states of the C 2 H molecule

Predissociation resonances in CO and IBr. Smooth exterior scaling combined with the discrete variable representation

Smooth exterior scaling (SES) and the discrete variable representation (DVR) are combined to accurately compute predissociation resonances of a bound state non-adiabatically coupled to a dissociative state. For the CO( predissociation interaction good agreement is found with approaches based on optical potentials and complex scaling. The comparison is done both in the diabatic and the adiabatic representation. The effect of the coupling strength in the IBr predissociation interaction and the transition from the diabatic to the adiabatic picture was studied by computing resonances for coupling strengths from up to . The transition from weak (diabatic) to strong (adiabatic) coupling was clearly seen. The intermediate case leads to a complicated resonance distribution. Comparison was made with recent studies using pump-probe spectroscopy [M. Shapiro, M.J.J. Vrakking, A. Stolow, J. Chem. Phys. 110, 2465 (1999)]. It was found that the overall features of the experiment could be explained from the resonance distribution, but for a detailed comparison more accurate potential energy surfaces and couplings are needed.

Ultraviolet photodissociation of HCl in selected rovibrational states: Experiment and theory

Experimental and theoretical methods have been applied to investigate the effect of internal parent excitation on the ultraviolet photodissociation dynamics of HCl (X 1Σ+) molecules. Jet-cooled H35Cl molecules within a time-of-flight mass spectrometer were prepared by infra-red absorption in the following quantum states: v=1, J=0 and J=5; v=2, J=0 and J=11; v=3, J=0 and J=7. The excited molecules were then photodissociated at λ∼235 nm and the Cl(2Pj) photofragments detected using (2+1) resonance enhanced multiphoton ionization. The results are presented as the fraction of total chlorine yield formed in the spin–orbit excited state, Cl(2P1/2). The experimental measurements are compared with the theoretical predictions from a time-dependent, quantum dynamical treatment of the photodissociation dynamics of HCl (v=1−3, J=0). These calculations involved wavepacket propagation using the ab initio potential energy curves and coupling elements previously reported by Alexander, Pouilly, and Duhoo [J. Chem. Phys. 99, 1752 (1993)]. The experimental results and theoretical predictions share a common qualitative trend, although quantitative agreement occurs only for HCl (v=2).

Influence of metastable states in electron capture processes

The influence of metastable states in electron capture processes is exhibited for the example of the N5+(1s2s)+He and B3+(1s2s)+H collisions. Ab initio calculations with configuration interaction have been used throughout for the determination of the potential energy curves and couplings of the states involved in the reactions. The collision dynamics has been performed by semi-classical methods in the keV energy range.

Quantum Wave Packet Study of Nonadiabatic Effects in O(1D) + H2 → OH + H

The authors develop a wave packet approach to treating the electronically nonadiabatic reaction dynamics of O({sup 1}D) + H{sub 2} {yields} OH + H, allowing for the 1{sup 1}A{prime} and 2{sup 1}A{prime} potential energy surfaces and couplings, as well as the three internal nuclear coordinates. Two different systems of coupled potential energy surfaces are considered, a semiempirical diatomics-in-molecules (DIM) system due to Kuntz, Niefer, and Sloan, and a recently developed ab initio system due to Dobbyn and Knowles (DK). Nonadiabatic quantum results, with total angular momentum J = 0, are obtained and discussed. Several single surface calculations are carried out for comparison with the nonadiabatic results. Comparisons with trajectory surface hopping (TSH) calculations, and with approximate quantum calculations, are also included. The electrostatic coupling produces strong interactions between the 1{sup 1}A{prime} and 2{sup 1}A{prime} states at short range (where these states have a conical intersection) and weak but, interestingly, nonnegligible interactions between these states at longer range. The wave packet results show that if the initial state is chosen to be effectively the 1A{prime} state (for which insertion to form products occurs on the adiabatic surface), then there is very little difference between the adiabatic and coupled surface results. Inmore » either case the reaction probability is a relatively flat function of energy, except for resonant oscillations. However, the 2A{prime} reaction, dynamics (which involves a collinear transition state) is strongly perturbed by nonadiabatic effects in two distinct ways. At energies above the transition state barrier, the diabatic limit is dominant, and the 2A{prime} reaction probability is similar to that for 1A{double{underscore}prime}, which has no coupling with the other surfaces. At energies below the barrier, the authors find a significant component of the reaction probability from long range electronic coupling that effectively allows the wave packet to avoid having to tunnel through the barrier. This effect, which is observed on both the DIM and DK surfaces, is estimated to cause a 10% contribution to the room temperature rate constant from nonadiabatic effects. Similar results are obtained from the TSH and approximate quantum calculations.« less

Are Semiclassical Methods Accurate for Electronically Nonadiabatic Transitions between Weakly Coupled Potential Energy Surfaces?

We have performed a systematic series of semiclassical and quantum mechanical calculations of collisions of Br* (electronicaly excited Br) with H2 in order to test four semiclassical methods against accurate quantum mechanical scattering calculations for the quenching probability and the electronically nonadiabatic reaction probability. The results are analyzed using four different methods of assigning final quantum numbers based on the final values of the semiclassical and classical trajectory variables, namely energy-nonconserving histogram analysis, energy-conserving histogram analysis, energy-nonconserving linear smooth sampling, and energy-conserving linear smooth sampling. We examine the use of both forward and reverse state-to-state probabilities to predict the quenching and reaction probabilities. The reaction and quenching probabilities are compared to the results of accurate quantum mechanical calculations, and the mean unsigned error is calculated for each combination of a semiclassical method and a final analysis algorithm. Our results indicate that Tully's fewest switches (TFS) trajectory-surface-hopping method and the Ehrenfest self-consistent-potential method show the best agreement with the accurate results, although none of the methods provides satisfactory agreement in the cases where the reaction or quenching probability is small. The TFS method is the only one that can be used to calculate the reaction probabilities for this system directly in the forward direction, and it is judged to be the best method overall for weakly coupled potential energy surfaces.

Density matrix theory and calculations of nonlinear yields of CO photodesorbed from Cu(001) by light pulses

The photodissociation of CO from Cu metal surfaces due to absorption of visible and ultraviolet (UV) light pulses is described within a density matrix approach, including the nonlinear optical response of the substrate to pulses of large fluence. We introduce a self-consistent coupling of adsorbate and substrate regions, and treat the substrate as a stochastic medium to account for dissipative effects following its electronic excitation. Our model is based on potential energy surfaces, couplings, and transition dipoles parametrized from electronic structure calculations for CO/Cu. The dynamics of photodesorption is obtained propagating wave packets with a nonperturbative treatment which includes the time dependence of the light pulse. Results have been obtained for the time evolution of state populations, and for yields of CO versus pulses fluence, with a range of values of the pulse width and light wavelength and of the dissipation time constant. Our numerical results for the desorption yields and desorption times are consistent with results of femtosecond photodesorption experiments at both low and high fluence values.

A classical-path surface-hopping study of Mu, H and T hot-atom collisions with F2

The collision dynamics of processes pertinent to the hot-atom chemistry of the hydrogen isotopes Mu, H and T with F2 are explored using mixed quantum–classical techniques. We use classical-path surface-hopping and pure classical-path multi-surface trajectory methods with a set of 14 coupled potential energy surfaces (PESs) from a diatomics-in-molecules (DIM) model. We compare with results from the standard quasiclassical trajectory (QCT) method applied to the electronic ground state surface of the same DIM model. We compute reaction- and dissociation cross sections for centre-of-mass collision energies ranging from threshold to 20 eV. In order to quantify the notion of electronic non-adiabaticity we introduce various cross sections measuring electronically non-adiabatic processes. We find that non-adiabatic effects give rise to pronounced changes in the dynamics of the Mu+F2 system. In particular, collision-induced dissociation of F2 by Mu is an essentially electronically non-adiabatic process, proceeding efficiently by a mechanism involving transitions to excited repulsive PESs. In contrast, QCT calculations on the electronic ground state surface predict vanishingly small Mu+F2 dissociation cross sections. We also discuss some consequences of this behaviour for simulations of Mu hot-atom chemistry.