Diabatic couplings for charge recombination via Boys localization and spin-flip configuration interaction singles

We describe a straightforward technique for obtaining diabatic couplings applicable to charge transfer from or charge recombination to the electronic ground state. Our method is nearly black box, requiring minimal chemical intuition from the user, and merges two well-established approaches in electronic structure theory: first, smooth and balanced adiabatic states are generated using spin-flip-configuration interaction singles (SF-CIS) based on a triplet HF state; second, Boys localization is applied to rotate all adiabatic states into charge-localized diabatic states. The method is computationally inexpensive, scaling only with the cost of CIS, and does not require a choice of active space, which is usually required for such intrinsically multiconfigurational problems. Molecular LiF in vacuum and LiF solvated by a single water molecule are examined as model systems. We find nearly smooth diabatic potential energy surfaces and couplings and we find that the Condon approximation is obeyed approximately for this model problem.     

Computer simulation of electron transfer processes across the electrode|electrolyte interface: a treatment of solvent and electrode polarizability

A polarizable molecular dynamics model for adiabatic electron transfer across the electrode|electrolyte interface is presented. The electronic polarizability of the water and of the metal electrode is accounted for by a dynamical fluctuating charge algorithm, image charges, and the Ewald summation adapted for a conducting interface. The effects of the solvent electronic polarizability are studied by computing the diabatic and adiabatic free energy curves for both polarizable and non-polarizable water models. This represents the first effort to compute the adiabatic free energy curves from simulation for a fully polarizable electrochemical system.     

Charge transfer ionic character illustration for strontium hydride ion through a diabatic investigation

Adiabatic and diabatic studies are performed for the strontium hydride ion (SrH)⁺. Potential energy surface and electric dipole moment for the ground and all excited states dissociating up to the charge transfer ionic limit Sr²⁺H⁻ have been investigated and analyzed in adiabatic and diabatic representations. The adiabatic approach uses the pseudo potential for the strontium atom complemented by core polarization potential operators, reducing the calculation to a two effective electrons system where full configuration interaction can be easily performed. The adiabatic results have been improved by a simple correction of the hydrogen electron affinity for all ¹Σ⁺ states. The diabatic results reveal the strong imprint of the charge transfer ionic state in the ¹Σ⁺ adiabatic states.     

Charge transfer in the electron donor-acceptor complex BH3NH3

As a simple yet strongly binding electron donor-acceptor (EDA) complex, BH(3)NH(3) serves as a good example to study the electron pair donor-acceptor complexes. We employed both the ab initio valence bond (VB) and block-localized wave function (BLW) methods to explore the electron transfer from NH(3) to BH(3). Conventionally, EDA complexes have been described by two diabatic states: one neutral state and one ionic charge-transferred state. Ab initio VB self-consistent field (VBSCF) computations generate the energy profiles of the two diabatic states together with the adiabatic (ground) state. Our calculations evidently demonstrated that the electron transfer between NH(3) and BH(3) falls in the abnormal regime where the reorganization energy is less than the exoergicity of the reaction. The nature of the NH(3)-BH(3) interaction is probed by an energy decomposition scheme based on the BLW method. We found that the variation of the charge-transfer energy with the donor-acceptor distance is insensitive to the computation levels and basis sets, but the estimation of the amount of electron transferred heavily depends on the population analysis procedures. The recent resurgence of interest in the nature of the rotation barrier in ethane prompted us to analyze the conformational change of BH(3)NH(3), which is an isoelectronic system with ethane. We found that the preference of the staggered structure over the eclipsed structure of BH(3)NH(3) is dominated by the Pauli exchange repulsion.     

On the construction of diabatic and adiabatic potential energy surfaces based on ab initio valence bond theory

A theoretical model is presented for deriving effective diabatic states based on ab initio valence bond self-consistent field (VBSCF) theory by reducing the multiconfigurational VB Hamiltonian into an effective two-state model. We describe two computational approaches for the optimization of the effective diabatic configurations, resulting in two ways of interpreting such effective diabatic states. In the variational diabatic configuration (VDC) method, the energies of the diabatic states are variationally minimized. In the consistent diabatic configuration (CDC) method, both the configuration coefficients and orbital coefficients are simultaneously optimized to minimize the adiabatic ground-state energy in VBSCF calculations. In addition, we describe a mixed molecular orbital and valence bond (MOVB) approach to construct the CDC diabatic and adiabatic states for a chemical reaction. Note that the VDC-MOVB method has been described previously. Employing the symmetric S(N)2 reaction between NH(3) and CH(3)NH(3)(+) as a test system, we found that the results from ab initio VBSCF and from ab initio MOVB calculations using the same basis set are in good agreement, suggesting that the computationally efficient MOVB method is a reasonable model for VB simulations of condensed phase reactions. The results indicate that CDC and VDC diabatic states converge, respectively, to covalent and ionic states as the molecular geometries are distorted from the minimum of the respective diabatic state along the reaction coordinate. Furthermore, the resonance energy that stabilizes the energy of crossing between the two diabatic states, resulting in the transition state of the adiabatic ground-state reaction, has a strong dependence on the overlap integral between the two diabatic states and is a function of both the exchange integral and the total diabatic ground-state energy.     

An Anderson impurity model for efficient sampling of adiabatic potential energy surfaces of transition metal complexes

We present a model intended for rapid sampling of ground and excited state potential energy surfaces for first-row transition metal active sites. The method is computationally inexpensive and is suited for dynamics simulations where (1) adiabatic states are required "on-the-fly" and (2) the primary source of the electronic coupling between the diabatic states is the perturbative spin-orbit interaction among the 3d electrons. The model Hamiltonian we develop is a variant of the Anderson impurity model and achieves efficiency through a physically motivated basis set reduction based on the large value of the d-d Coulomb interaction U(d) and a Lanczos matrix diagonalization routine to solve for eigenvalues. The model parameters are constrained by fits to the partial density of states obtained from ab initio density functional theory calculations. For a particular application of our model we focus on electron transfer occurring between cobalt ions solvated by ammonium, incorporating configuration interaction between multiplet states for both metal ions. We demonstrate the capability of the method to efficiently calculate adiabatic potential energy surfaces and the electronic coupling factor we have calculated compares well to previous calculations and experiment. (     

Interpolation of diabatic potential energy surfaces

A method is presented for constructing diabatic potential energy matrices from ab initio quantum chemistry data. The method is similar to that reported previously for single adiabatic potential energy surfaces, but correctly accounts for the nuclear permutation symmetry of diabatic potential energy matrices and other complications that arise from the derivative coupling of electronic states. The method is tested by comparison with an analytic model for the two lowest energy states of H(3).     

Electronic coupling for charge transfer in donor-bridge-acceptor systems. Performance of the two-state FCD model

Electronic coupling is a key parameter that determines the rate of electron transfer reactions and electrical conductivity of molecular wires. To examine the performance of a two-state approach based on the orthogonal transformation of adiabatic states to diabatic states, we compare the effective donor-acceptor coupling V(DA) computed with three different approaches in model donor-bridge-acceptor (D-B-A) systems. It is found that V(DA) derived with the two-state method accounts properly for both the direct and superexchange interactions. The approach becomes, however, less accurate with the increasing energy difference of the donor and acceptor states. We suggest a simple diagnostic to identify the situation when the estimated coupling might be inaccurate and consider how to improve the performance of the two-state scheme in such a case.     

Linking the historical and chemical definitions of diabatic states for charge and excitation energy transfer reactions in condensed phase

Marcus theory of electron transfer (ET) and Fo?rster theory of excitation energy transfer (EET) rely on the Condon approximation and the theoretical availability of initial and final states of ET and EET reactions, often called diabatic states. Recently [Subotnik et al., J. Chem. Phys. 130, 234102 (2009)], diabatic states for practical calculations of ET and EET reactions were defined in terms of their interactions with the surrounding environment. However, from a purely theoretical standpoint, the definition of diabatic states must arise from the minimization of the dynamic couplings between the trial diabatic states. In this work, we show that if the Condon approximation is valid, then a minimization of the derived dynamic couplings leads to corresponding diabatic states for ET reactions taking place in solution by diagonalization of the dipole moment matrix, which is equivalent to a Boys localization algorithm; while for EET reactions in solution, diabatic states are found through the Edmiston-Ruedenberg localization algorithm. In the derivation, we find interesting expressions for the environmental contribution to the dynamic coupling of the adiabatic states in condensed-phase processes. In one of the cases considered, we find that such a contribution is trivially evaluable as a scalar product of the transition dipole moment with a quantity directly derivable from the geometry arrangement of the nuclei in the molecular environment. Possibly, this has applications in the evaluation of dynamic couplings for large scale simulations.     

Neutral organic mixed-valence compounds: synthesis and all-optical evaluation of electron-transfer parameters

In this paper we present the synthesis as well as a detailed study of the electrochemical and photophysical properties of a series of neutral organic mixed-valence (MV) compounds, 1-7, in which different amine donor centers are connected to perchlorinated triarylmethyl radical units by various spacers. We show that this new class of compounds are excellent model systems for the investigation of electron transfer due to their uncharged character and, consequently, their excellent solubility, particularly in nonpolar solvents. A detailed band shape analysis of the intervalence charge-transfer (IV-CT) bands in the context of Jortner's theory allowed the electron-transfer parameters (inner vibrational reorganization energy lambdav, outer solvent reorganization energy lambdao, and the difference in the free energy between the diabatic ground and excited states, DeltaG degrees degrees , as well as the averaged molecular vibrational mode v) to be extracted independently. In this way we were able to analyze the solvatochromic behavior of the IV-CT bands by evaluating the contribution of each parameter. By comparison of different compounds, we were also able to assign specific molecular moieties to changes in vv. For this class of molecules, we also demonstrate that the adiabatic dipole moment difference Deltamicroab and, consequently, the electronic coupling V12 can be evaluated directly from the absorption spectra by a new variant of the solvatochromic method. Furthermore, an investigation of the electrochemistry of compounds 1-7 by cyclic voltammetry as well as spectroelectrochemistry shows that, not only in the neutral MV compounds but also in their oxidized forms, a charge transfer can be optically induced but with exchanged donor-acceptor functionalities of the redox centers.     

Surface hopping simulation of vibrational predissociation of methanol dimer

The mixed quantum-classical surface hopping method is applied to the vibrational predissociation of methanol dimer, and the results are compared to more exact quantum calculations. Utilizing the vibrational SCF basis, the predissociation problem is cast into a curve crossing problem between dissociative and quasibound surfaces with different vibrational character. The varied features of the dissociative surfaces, arising from the large amplitude OH torsion, generate rich predissociation dynamics. The fewest switches surface hopping algorithm of Tully [J. Chem. Phys. 93, 1061 (1990)] is applied to both diabatic and adiabatic representations. The comparison affords new insight into the criterion for selecting the suitable representation. The adiabatic method's difficulty with low energy trajectories is highlighted. In the normal crossing case, the diabatic calculations yield good results, albeit showing its limitation in situations where tunneling is important. The quadratic scaling of the rates on coupling strength is confirmed. An interesting resonance behavior is identified and is dealt with using a simple decoherence scheme. For low lying dissociative surfaces that do not cross the quasibound surface, the diabatic method tends to overestimate the predissociation rate whereas the adiabatic method is qualitatively correct. Analysis reveals the major culprits involve Rabi-like oscillation, treatment of classically forbidden hops, and overcoherence. Improvements of the surface hopping results are achieved by adopting a few changes to the original surface hopping algorithms.     

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.     

Electron transfer within 2,7-dinitronaphthalene radical anion

The optical spectrum of 2,7-dinitronaphthalene radical anion generated by Na(Hg) reduction in acetonitrile containing a large excess of cryptand[2.2.2] exhibits a Hush-type intervalence charge-transfer band at 1070 nm, estimated to correspond to an off-diagonal matrix coupling element of 310 cm(-)(1). The interpolated rate constant for intramolecular electron transfer at 293 K measured by ESR between 225 and 320 K for this solution is 3.1(+/-0.2) x 10(9) s(-)(1). Rate constants estimated in two ways from the optical parameters using the Marcus-Hush assumption that the diabatic surfaces should be parabolae are 1.0 and 0.11 x 10(9) s(-1), and those using diabatic surfaces that fit the observed charge-transfer band are 9.6 and 3.4 x 10(9) s(-)(1), when used with an electron-transfer distance on the adiabatic surfaces of 6.42 A. Similar measurements and comparisons were also carried out using dimethylformamide and butyronitrile as solvents. The success of simple, classical two-state Marcus-Hush theory precludes an electron-hopping mechanism. UHF calculations predict a planar unsymmetrical gas-phase structure for 1,3-dinitrobenzene radical anion but give serious spin contamination. Semiempirical AM1 calculations using singles excitation configuration interaction with an active space of 70 orbitals and the COSMO solvent model also give a planar unsymmetrical structure. These calculations make the internal vibrational component of the reorganization energy nearly constant, and much smaller than the solvent reorganizational component, and predict the transition energy to lie between that observed in acetonitrile (9360 cm(-1)) and those observed in dimethylformamide (8100 cm(-1)) and butyronitrile (8040 cm(-1)).     

Electron Correlation Effects for Adiabatic Electrochemical Reactions of Electron Transfer in a Model for an Electrode with an Infinitely Wide Conduction Band: Computing Adiabatic Free Energy Surfaces

The adiabatic free energy surfaces for adiabatic electrochemical reactions of electron transfer are calculated in a model for an electrode with an infinitely wide conduction band with exact allowance for electron–electron correlations. The surfaces are analyzed on the basis of a diagram of kinetic modes obtained earlier. It is shown that, as in a surface-molecule model for these reactions, the correlation effects play an essential role and lead to a considerable decrease in the activation free energies and to qualitatively different forms of adiabatic free energy surfaces in certain ranges of model parameters.     

On the fine-structure dependence of the Cs(7p, 2P12,320)+H2→ CsH+H reaction cross section

The experimentally observed effect of the Cs¹ fine-structure level on the title reaction is reproduced by a rough (collinear, one dimensional) dynamical treatment using accurate long-distance entrance channel potentials, as obtained from an effective Hamiltonian method, and hemiquantal dynamics in the collision energy range 0.03 to 0.13 eV. The system is shown to behave adiabatically at large distances, to undergo a transition from adiabatic to diabatic behaviour with respect to spin-orbit coupling in the 11–8.5 au Cs-H distance range, and to transfer adiabatically the whole ²Σ⁺ weight of the electronic wavefunction into theionic channel in the harpooning region.     

Proton-coupled electron transfer versus hydrogen atom transfer: generation of charge-localized diabatic states

The distinction between proton-coupled electron transfer (PCET) and hydrogen atom transfer (HAT) mechanisms is important for the characterization of many chemical and biological processes. PCET and HAT mechanisms can be differentiated in terms of electronically nonadiabatic and adiabatic proton transfer, respectively. In this paper, quantitative diagnostics to evaluate the degree of electron-proton nonadiabaticity are presented. Moreover, the connection between the degree of electron-proton nonadiabaticity and the physical characteristics distinguishing PCET from HAT, namely, the extent of electronic charge redistribution, is clarified. In addition, a rigorous diabatization scheme for transforming the adiabatic electronic states into charge-localized diabatic states for PCET reactions is presented. These diabatic states are constructed to ensure that the first-order nonadiabatic couplings with respect to the one-dimensional transferring hydrogen coordinate vanish exactly. Application of these approaches to the phenoxyl-phenol and benzyl-toluene systems characterizes the former as PCET and the latter as HAT. The diabatic states generated for the phenoxyl-phenol system possess physically meaningful, localized electronic charge distributions that are relatively invariant along the hydrogen coordinate. These diabatic electronic states can be combined with the associated proton vibrational states to generate the reactant and product electron-proton vibronic states that form the basis of nonadiabatic PCET theories. Furthermore, these vibronic states and the corresponding vibronic couplings may be used to calculate rate constants and kinetic isotope effects of PCET reactions.     

X-ray absorption and resonant Auger spectroscopy of O2 in the vicinity of the O 1s-->sigma* resonance: experiment and theory

We report on an experimental and theoretical investigation of x-ray absorption and resonant Auger electron spectra of gas phase O(2) recorded in the vicinity of the O 1s-->sigma(*) excitation region. Our investigation shows that core excitation takes place in a region with multiple crossings of potential energy curves of the excited states. We find a complete breakdown of the diabatic picture for this part of the x-ray absorption spectrum, which allows us to assign an hitherto unexplained fine structure in this spectral region. The experimental Auger data reveal an extended vibrational progression, for the outermost singly ionized X (2)Pi(g) final state, which exhibits strong changes in spectral shape within a short range of photon energy detuning (0 eV>Omega>-0.7 eV). To explain the experimental resonant Auger electron spectra, we use a mixed adiabatic/diabatic picture selecting crossing points according to the strength of the electronic coupling. Reasonable agreement is found between experiment and theory even though the nonadiabatic couplings are neglected. The resonant Auger electron scattering, which is essentially due to decay from dissociative core-excited states, is accompanied by strong lifetime-vibrational and intermediate electronic state interferences as well as an interference with the direct photoionization channel. The overall agreement between the experimental Auger spectra and the calculated spectra supports the mixed diabatic/adiabatic picture.     

Spectroscopic consequences of a mixed valence excited state: quantitative treatment of a dihydrazine diradical dication

A model for the quantitative treatment of molecular systems possessing mixed valence excited states is introduced and used to explain observed spectroscopic consequences. The specific example studied in this paper is 1,4-bis(2-tert-butyl-2,3-diazabicyclo[2.2.2]oct-3-yl)-2,3,5,6-tetramethylbenzene-1,4-diyl dication. The lowest energy excited state of this molecule arises from a transition from the ground state where one positive charge is associated with each of the hydrazine units, to an excited state where both charges are associated with one of the hydrazine units, that is, a Hy-to-Hy charge transfer. The resulting excited state is a Class II mixed valence molecule. The electronic emission and absorption spectra, and resonance Raman spectra, of this molecule are reported. The lowest energy absorption band is asymmetric with a weak low-energy shoulder and an intense higher energy peak. Emission is observed at low temperature. The details of the absorption and emission spectra are calculated for the coupled surfaces by using the time-dependent theory of spectroscopy. The calculations are carried out in the diabatic basis, but the nuclear kinetic energy is explicitly included and the calculations are exact quantum calculations of the model Hamiltonian. Because the transition involves the transfer of an electron from the hydrazine on one side of the molecule to the hydrazine on the other side and vice versa, the two transitions are antiparallel and the transition dipole moments have opposite signs. Upon transformation to the adiabatic basis, the dipole moment for the transition to the highest energy adiabatic surface is nonzero, but that for the transition to the lowest surface changes sign at the origin. The energy separation between the two components of the absorption spectrum is twice the coupling between the diabatic basis states. The bandwidths of the electronic spectra are caused by progressions in totally symmetric modes as well as progressions in the modes along the coupled coordinate. The totally symmetric modes are modeled as displaced harmonic oscillators; the frequencies and displacements are determined from resonance Raman spectra. The absorption, emission, and Raman spectra are fit simultaneously with one parameter set. The coupling in the excited electronic state H(ab)(ex) is 2000 cm(-1). Excited-state mixed valence is expected to be an important contributor to the electronic spectra of many organic and inorganic compounds. The energy separations and relative intensities enable the excited-state properties to be calculated as shown in this paper, and the spectra provide new information for probing and understanding coupling in mixed valence systems.