Diabatic Curves Research Articles

Insights into dioxygen binding on metal centers: an ab initio multireference electronic structure analysis.

Why does binding of dioxygen (O2) to metal centers, the initial step of O2 storage, transportation, and activation, almost inevitably induce metal-to-O2 single-electron transfer and generate superoxo (O2-˙) species, instead of genuine O02 adducts? To address this question, this study describes highly correlated wavefunction-based ab initio calculations using CASSCF/NEVPT2 (CASSCF = complete active space self-consistent field, and NEVPT2 = N-electron valence state second-order perturbation theory) approaches to explore the electronic-structure evolution of O2 association on Fe(II)(BDPP) (H2BDPP = 2,6-bis((2-(S)-diphenylhydroxylmethyl-1-pyrrolidinyl)methyl)pyridine) and Co(II)(BDPP) to produce S = 3 Fe(III)(BDPP)(O2-˙) (1) and Co(III)(BDPP)(O2-˙) (2). CASSCF/NEVPT2 calculations suggest that the processes furnishing 1 and 2 feature an avoided crossing resulting from interactions of two diabatic curves, of which one is characterized as Co(II) and Fe(II) centers interacting with a triplet O2 ligand and the other as Co(III) and Fe(III) centers bound to a superoxo ligand. In both cases, the avoided crossing induces a one-electron transfer from the divalent metal center to the incoming O2 ligand and leads to formation of trivalent metal-O2-˙ complexes. To facilitate the interpretation of complicated multireference wavefunctions, we formulated two-fragment spin eigenfunctions utilizing Clebsch-Gordan coefficients (CGCs) to rationalize computed spin populations on the metal centers and the O2 ligand and compared these results with usual valence bonding (VB) analyses. It turns out that both methods give the same results and are complementary to each other. Finally, the limitation of DFT approaches in describing complex electronic structures involving metal-ligand magnetic couplings is delineated.

CH4, an ab initio story of an archetypal species.

The methane molecule is an archetypal species in the whole of chemistry for its ability to form four bonds that result in a myriad of compounds of chemical and biological importance. The hybrid orbitals involved in the bonding have been scrutinized for too many decades but only lately under the ab initio microscope. In this study, we detail the formation routes CHn + (4 - n) H → CH4 (n = 0, 1, and 2) both diabatically and adiabatically with the help of established computational techniques. The evolution of the Mulliken populations, of the non-adiabatic matrix coupling elements, and of the Kotani spin functions along the dissociation paths and finally the shape of the diabatic curves unambiguously point to a parental C atom of an excited 2s12p3 electronic configuration.

Role of Overlap between the Discrete State and Pseudocontinuum States in Stabilization Calculations of Metastable States.

In a diabatic picture metastable states subject to decay by electron detachment can be viewed as arising from the coupling between a discrete state and a continuum. In treating such states with bound-state quantum chemical methods, the continuum is discretized. In this study, we elucidate the role of overlap in this interaction in the application of the stabilization method to temporary anion states. This is accomplished by use of a minimalist stabilization calculation on the lowest energy (D) resonance of the finite spherical well potential using two basis functions, one describing the diabatic discrete state and the other a diabatic discretized continuum state. We show that even such a simple treatment predicts a complex resonance energy in good agreement with the exact result. If the energy of the discrete state is assumed to be constant, which is tantamount to orthogonalizing the discretized continuum state to the discrete state, it is demonstrated that the square of the off-diagonal coupling has a maximum close to the crossing point of the orthogonalized diabatic curves and that the curvature in the coupling is responsible for the complex stationary point associated with the resonance. Moreover, this curvature is a consequence of the overlap between the two diabatic states.

Temperature dependence of dissociative electron attachment to bromo-chlorotoluene isomers: Competition between detachment of Cl- and Br.

Dissociative electron attachment to three isomers of bromo-chlorotoluene was investigated in the electron energy range from 0 to 2 eV for gas temperatures in the range of 392-520 K using a crossed electron-molecular beam apparatus with a temperature regulated effusive molecular beam source. For all three molecules, both Cl- and Br- are formed. The ion yields of both halogenides show a pronounced temperature effect. In the case of Cl- and Br-, the influence of the gas temperature can be observed at the threshold peak close to 0 eV. The population of molecules that have some of their out-of-plane modes excited varies strongly in the temperature range investigated, indicating that such vibrations might play a role in the energy transfer towards bond breaking. Potential energy curves for the abstraction of Cl- and Br- were calculated and extrapolated into the metastable domain. The barriers in the diabatic curves approximated in this way agree well with the ones derived from the temperature dependence observed in the experiments.

The vibrational relaxation of NO in Ar: tunneling in a curve-crossing mechanism.

Experimental data for the vibrational relaxation NO(X(2)Π, v = 1) + Ar → NO(X(2)Π, v = 0) + Ar between 300 and 2000 K are analyzed. The measured rate coefficients k10 greatly exceed Landau-Teller values (LT)k10. This observation can be attributed to a mechanism involving curve-crossing of the (A'', v = 1) and (A', v = 0) vibronic states of the collision system. At high temperatures, the rate coefficients k10 are well represented by the thermally averaged Landau-Zener rate constant (LZ)k10 with an apparent Arrhenius activation energy Ea/kB near 4500 K. At intermediate temperatures, around T = 900 K, the measured k10 values are a factor of two higher than the extrapolated (LZ)k10 values. This deviation is attributed to tunneling in nonadiabatic curve-crossing transitions, which are analyzed within the Airy approximation (linear model for crossing diabatic curves) and an effective mass approach. This suggests a substantial contribution of hindered rotation of NO to the nonadiabatic perturbation. The extrapolation of the Airy probabilities to even lower temperatures (by the Landau-Lifshitz WKB tunneling expression for simple nonlinear model potentials) indicates a further marked increase of the tunneling contribution beyond the extrapolated (LZ)k10. Near 300 K, the k10 can be two to three orders of magnitude higher than the extrapolated (LZ)k10. This agrees with the limited available experimental data for NO-Ar relaxation near room temperature.

Some remarks on the selection of exit channels in the theoretical description of dissociative recombination

The need for the careful selection of dissociative routes for inclusion in the theoretical calculation of accurate dissociative recombination (DR) cross sections and rate constants is discussed. For total energies corresponding to the sum of the “free” electron energy plus the ion vibrational energy, all neutral diabatic curves that fall between or near the turning points of the highest Rydberg vibrational levels with the same electronic symmetry need to be included in the calculation. This is especially the case if there are several dissociative routes of the same electronic symmetry that satisfy this criterion. Also, care must be exercised in the exclusion of dissociative routes having relatively small electron capture widths. Examples from theoretical studies of the dissociative recombination (DR) of N2 + are used as illustrations.

Understanding the structure and electronic properties of Th4+-water complexes

We present a systematic quantum chemistry study of the [Th(H2O)n]4+(n = 1 to 10) complexes to gain insight into their electronic structure and properties: the effect of the ligand distribution on the valence shells of the thorium(IV) ion is studied by means of the electron localization function (ELF) topological analysis. Particular care is given to the study of the mono-aqua complex both at its equilibrium geometry, using various tools such as energy decomposition analyses (EDA), and along its dissociation pathway. Indeed, as several electronic states cross the Th4 +-H2O0ground state along the minimum energy path, we demonstrate that the diabatic representation implemented in MOLPRO is able to generate reference potential energy surfaces that will lead to the evaluation of diabatic dissociation curves. The calculated diabatic interaction energy curve will allow for a consistent parameterization of new generation force fields dedicated to heavy metals based on quantum chemistry.

Ab Initio Adiabatic and Diabatic Energies and Dipole Moments of the CaH+ Molecular Ion

The diabatic and adiabatic potential-energy curves and permanent and transition dipole moments of the highly excited states of the CaH(+) molecular ion have been computed as a function of the internuclear distance R for a large and dense grid varying from 2.5 to 240 au. The adiabatic results are determined by an ab initio approach involving a nonempirical pseudopotential for the Ca core, operatorial core-valence correlation, and full valence configuration interaction. The molecule is thus treated as a two-electron system. The diabatic potential energy curves have been calculated using an effective metric combined to the effective Hamiltonian theory. The diabatic potential-energy curves and their permanent dipole moments for the (1)∑(+) symmetry are examined and corroborate the high imprint of the ionic state in the adiabatic representation. Taking the benefit of the diabatization approach, correction of hydrogen electron affinity was taken into account leading to improved results for the adiabatic potentials but also the permanent and transition electric dipole moments.

Is There Symmetry Breaking in the First Excited Singlet State of 2-Pyridone Dimer?

We investigate the S(1) state potential energy surface of 2-pyridone dimer (2PY)(2) using time-dependent density functional and coupled cluster theory. Although the ground and S(2) excited states of (2PY)(2) have C(2h) symmetry, the S(1) state shows symmetry breaking and localization of the excitation on one of the two monomers upon relaxation of the geometry. This localization is rationalized using a simple diabatic curve crossing model. As a consequence of the symmetry breaking, S(1) to S(0) transitions become optically allowed. We hypothesize that the band at 30,776 cm(-1) observed in the excitation spectrum of (2PY)(2) might be attributed to the S(1) state rather than the S(2) state; the S(2) state origin is predicted 3000-4000 cm(-1) above the S(1) state by hybrid density functional and coupled cluster methods. Asymmetric transfer of one hydrogen atom leads to a second S(1) state minimum that can rapidly decay to the ground state. This suggests that photoinduced tautomerization of (2PY)(2) occurs in a stepwise fashion, with only one hydrogen transfer taking place on the S(1) surface.

An interpretation of the anomalous Π1 vibronic structure in the far-UV spectrum of CO

The far-UV spectrum of carbon monoxide presents numerous abnormal (1)Pi rovibronic levels in the region 92,000-105,000 cm(-1) which have been observed by several experimentalists. Yet, and in spite of various attribution attempts carried out over the past two decades, the nature of these levels is poorly understood and they still lack a definitive assignment. The absorption lines in this energy region are characterized by irregular energy level positions and spacings, and odd, smaller than expected, rotational constants. In the current contribution we address this puzzle by relying on recent ab initio calculations of several Rydberg and valence states of CO [G. J. Vazquez, J. M. Amero, H. P. Liebermann, and H. Lefebvre-Brion, J. Phys. Chem. A 113, 13395 (2009)], and on further new calculations in which we compute electronic transition moments between the ground state and several excited (1)Pi states. We focus on the perturbations between the adiabatic (1)Pi states, specifically on the interaction between the second and third potential energy curves, reported in our previous paper. The second adiabatic potential energy curve, which we refer to as E-E('), displays a distorted shape with two minima as a result of an avoided crossing with the third one. We report here the computation of the lowest vibronic levels of a system of two electronic states which undergo a strong Rydberg-valence interaction. Our vibronic calculations proceed as follows: from the second and third computed adiabatic curves we first obtain approximate diabatic curves for the (X (2)Sigma(+))3ppi E (1)Pi Rydberg state and for the valence E(') (1)Pi state. Then we solve a system of 2x2 coupled equations in order to obtain the perturbed vibronic energy levels and wave functions for the interacting E and E(') states. The computed vibronic levels obtained from the coupled equation treatment are compared to the first six observed (1)Pi levels. A good agreement is found with experiment for the four lowest vibronic levels and a reasonable accord for two higher levels.

Rapid adiabatic passage without level crossing

We present a method for achieving complete population transfer in a two-state quantum system via adiabatic time evolution in which, contrary to conventional rapid adiabatic passage produced by chirped pulses, there occurs no crossing of diabatic energy curves: there is no sign change of the detuning. Instead, we use structured pulses, in which, in addition to satisfying conditions for adiabatic evolution, there occurs a sign change of the Rabi frequency when the detuning is zero. We present simulations that offer simple geometrical interpretation of the two-dimensional motion of the Bloch vector for this system, illustrating how both complete population inversion and complete population return occur for different choices of structured pulses.

Cuaq+/Cuaq2+ Redox Reaction Exhibits Strong Nonlinear Solvent Response Due to Change in Coordination Number

We have carried out extensive Born-Oppenheimer molecular dynamics simulations to characterize the structure and energetics of the Cu(+)/Cu(2+) redox pair. Our simulations support recent experimental evidence suggesting that Cu(2+) adopts a 5-fold coordination in aqueous solution and not the traditionally assumed octahedral coordination. Cu(+) forms a linear dihydrate structure with a third water molecule occasionally binding in the equatorial plane. We show that the change in ligand coordination number from 2 for aqueous Cu(+) to 5 for aqueous Cu(2+) leads to marked deviations from the linear response assumption underlying Marcus theory of oxidation. The diabatic free energy curves deviate from parabolic behavior and the reorganization free energies for Cu(+) and Cu(2+) are asymmetric and differ by 1.0 eV. The calculated reorganization free energies can semiquantitatively explain the exceptionally small electron self-exchange rate between Cu(+) and Cu(2+) in aqueous solution.

Multiple occurrence of zero-width resonances in photodissociation: Effect of laser field intensity and frequency

Critical intensities at which the strong field photodissociation rates of a molecule are vanishing could play an important role in control scenarios to filter a given vibrational state. We have previously shown [O. Atabek, R. Lefebvre, and F. Gad\'ea, Phys. Rev. A 74, 063412 (2006)] that there is a multiplicity of such intensities when the diabatic curve crossing point is on the left of the minimum of the attractive potential in a photon dressed picture (${c}^{\ensuremath{-}}$ case). A semiclassical explanation was given. We complete this study of the multiple occurrence of zero-width resonances (ZWRs) by addressing, both numerically and semiclassically, the more common ${c}^{+}$ case of a crossing point on the right of the potential minimum. Coincidences between modified diabatic and adiabatic levels are the fingerprints of such events. They occur several times because the adiabatic energies are moving upward more rapidly than the diabatic ones. Advantage can be taken of the frequency dependence of the critical intensities to produce the phenomenon even for weak fields, this circumstance leading to more favorable control issues. This is illustrated on the example of ${\mathrm{H}}_{2}^{+}$. The wave functions associated with the ZWRs reflect the fact that the adiabatic picture is the best zeroth order description in the limit of high fields.

Controlling spin contamination using constrained density functional theory

We have extended the constrained density functional theory (DFT) approach to explicitly control the magnitude of spin contamination. Unlike a restricted or restricted open-shell approach, the present method allows finer granularity, not only constraining the magnitude of the spin contamination but also allowing for the possibility of applying the constraint to a subsystem of a much larger system. This allows for the description of spin polarization where physically meaningful, while simultaneously enabling the reduction of spurious overpolarization that is present in many DFT functionals. We utilize this constraint in two particular model applications: The calculation of isotropic and anisotropic hyperfine couplings of a transition metal complex, [Mn(CN)(5)NO](2-), and the calculation of the diabatic dissociation curves of OF radical. In both cases, the spin contamination constraint is essential for obtaining physically meaningful, qualitatively correct, results.

Theoretical Investigation of Femtosecond-Resolved Photoelectron Spectrum of NaI Molecules

The time-resolved photoelectron spectra (TRPES) of NaI molecules are calculated by using the time-dependent wave packet method. Two different potential energy curves (adiabatic and diabatic) are adopted in the simulation. The third peak of the photoelectron spectra presented in the adiabatic calculation is induced by the reflection of the wave packet. The oscillating of the wave packet onto the diabatic energy curve is a decreasing process. The comparison of the photoelectron spectra between the two different calculations (adiabatic and diabatic) is presented.

Electron-Transfer Reactions in Supercritical Water

Free energies and dynamics of electron-transfer reactions for a diatomic donor-acceptor complex in ambient and supercritical water are studied via molecular dynamics computer simulations using a two-state electronic description. The free energy perturbation method is employed to examine diabatic electronic curves relevant to charge separation and recombination and electron self-exchange. It is found that the diabatic curves are anharmonic and vary with the charge distributions of the donor-acceptor complex, consonant with earlier studies under ambient conditions. Nonetheless, the extent of their anharmonicity and dependence on charge distributions grows with decreasing solvent density so that the Marcus free energy relationship breaks down in low-density supercritical water. The influence of solvent dynamics associated with activation, deactivation, and adiabatic barrier crossing on reaction kinetics is analyzed. Although the transition state theory generally provides a reasonable framework to describe electron-transfer kinetics in a wide range of thermodynamic conditions, the deviation of the reaction rate from the transition state theory predictions increases as the water density decreases.

Free Energy and Dynamics of Electron-Transfer Reactions in a Room Temperature Ionic Liquid

Reaction free energetics and dynamics of unimolecular electron-transfer processes in ionic liquid 1-ethyl-3-methylimidazolium hexafluorophosphate (EMI+PF6-) are investigated via molecular dynamics computer simulations employing a model diatomic solute and compared with those in aprotic acetonitrile. Using the free energy perturbation method, diabatic free energy curves relevant to charge separation and recombination processes are studied over a wide range of the reaction coordinate. The diabatic curves are found to vary with the solute charge distribution, especially in EMI+PF6-. Nevertheless, if the free energy of reaction is not that substantial, the Marcus free energy relationship holds reasonably well, provided that the reorganization free energy averaged between the reactant and product states is employed. The effective polarity, measured as solvation-induced stabilization of dipolar solutes, is higher for EMI+PF6- than for acetonitrile, consonant with many solvatochromic measurements. Thus, in the normal regime, activation barriers for charge separation and recombination reactions are, respectively, lower and higher in EMI+PF6- than in acetonitrile. The influence of solvent dynamics on reaction kinetics through modulations of activation, deactivation, and barrier crossing is analyzed. Even though overall solvent relaxation dynamics in EMI+PF6- are considerably slower than those in acetonitrile, the deviation of the rate constant from the transition state theory predictions is found to be small for both solvents. Implications of this finding for other reactions in ionic liquids are briefly discussed.

Electron promotion and electronic friction in atomic collision cascades

We present a computer simulation model for the space- and time-resolved calculation of electronic excitation energy densities in atomic collision cascades. The model treats electronic friction as well as electron promotion as a source term of electronic energy that is carried away from the original point of excitation according to a nonlinear diffusion equation. While the frictional source is treated within the Lindhard model of electronic stopping, electron promotion is described using diabatic correlation curves derived from ab initio molecular orbital energy level calculations in combination with the Landau–Zener curve crossing model. Results calculated for two selected collision cascades show that the electron promotion mechanism may contribute significantly to the excitation energy density in the cascade volume, giving rise to distinct peaks of the local electron temperature at the surface. This contribution is essentially restricted to the first 100 fs after the projectile impact and may therefore be of significance for either external or internal kinetic electron emission. At later times, where the bombardment-induced particle kinetics lead to the sputter ejection of material from the surface, the excitation is shown to be primarily governed by electronic friction. This finding is important in light of excitation and ionization probabilities of sputtered particles.

Diabatic free energy curves and coordination fluctuations for the aqueous Ag+∕Ag2+ redox couple: A biased Born-Oppenheimer molecular dynamics investigation

Biased Born-Oppenheimer molecular dynamics simulations are performed to compute redox potential and free energy curves for the redox half reaction Ag(+)-->Ag(2+)+e(-) in aqueous solution. The potential energy surfaces of reactant and product state are linearly coupled and the system transferred from the reduced state to the oxidized state by variation of the coupling parameter from 0 to 1. The redox potential is obtained by thermodynamic integration of the average ionization energy of Ag(+). Diabatic free energy curves of reduced (R) and oxidized (O) states are obtained to good statistical accuracy by reweighting and combining the set of biased distributions of the ionization energy. The diabatic free energy curves of Ag(+) and Ag(2+) are parabolic over a wide range of the reaction coordinate in agreement with the linear response assumption that underlies Marcus theory. However, we observe deviations from parabolic behavior in the equilibrium region of Ag(+) and find different values for the reorganization free energy of R (1.4 eV) and O (0.9 eV). The computed reorganization free energy of Ag(2+) is in good agreement with the experimental estimate of 0.9-1.2 eV obtained from photoelectron spectroscopy. As suggested by our calculations, the moderate deviation from linear response behavior found for Ag(+) is likely related to the highly fluxional solvation shell of this ion, which exhibits water exchange reactions on the picosecond time scale of the present molecular dynamics simulation.

Quantum versus classical electron transfer energy as reaction coordinate for the aqueous Ru2+/Ru3+ redox reaction

Applying density functional theory (DFT)-based molecular dynamics simulation methods we investigate the effect of explicit treatment of electronic structure on the solvation free energy of aqueous Ru2+ and Ru3+.Our approach is based on the Marcus theory of redox half reactions, focussing on the vertical energy gap for reduction or oxidation of a single aqua ion. We compare the fluctuations of the quantum and classical energy gap along the same equilibrium ab initio molecular dynamics trajectory for each oxidation state. The classical gap is evaluated using a standard point charge model for the charge distribution of the solvent molecules (water). The quantum gap is computed from the full DFT electronic ground state energies of reduced and oxidized species, thereby accounting for the delocalization of the electron in the donor orbital and reorganization of the electron cloud after electron transfer (ET). The fluctuations of the quantum ET energy are well approximated by gaussian statistics giving rise to parabolic free energy profiles. The curvature is found to be independent of the oxidation state in agreement with the linear response assumption underlying Marcus theory. By contrast, the diabatic free energy curves evaluated using the classical gap as order parameter, while also quadratic, are asymmetric reflecting the difference in oxidation state. The response of these two order parameters is further analysed by a comparison of the spectral density of the fluctuations and the corresponding reorganization free energies.