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.     

A three-state effective Hamiltonian for symmetric cationic diarylmethanes

We analyze the low-energy electronic structure of a series of symmetric cationic diarylmethanes, which are bridge-substituted derivatives of Michler's Hydrol Blue. We use a four-electron, three-orbital complete active space self-consistent field and multi-state multi-reference perturbation theory model to calculate a three-state diabatic effective Hamiltonian for each dye in the series. We exploit an isolobal analogy between the active spaces of the self-consistent field solutions for each dye to represent the electronic structure in a set of analogous diabatic states. The diabatic states can be identified with the bonding structures in classical resonance-theoretic models of cyanine dyes. We identify diabatic states with opposing charge and bond-order localization, analogous to the classical resonance structures, and a third state with charge on the bridge. While the left- and right-charged structures are similar for all dyes, the structure of the bridge-charged diabatic state, and the Hamiltonian matrix elements connected to it, change significantly across the series. The change is correlated with an inversion of the sign of the charge carrier on the bridge, which changes from an electron pair to a hole as the series is traversed.     

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.     

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. (     

Renner-Teller and spin-orbit vibronic coupling effects in linear triatomic molecules with a half-filled pi shell

The vibronic and spin-orbit-induced interactions among the (3)Sigma(-), (1)Delta, and (1)Sigma(+) electronic states arising from a half-filled pi orbital of a linear triatomic molecule are considered, employing the microscopic (Breit-Pauli) spin-orbit coupling operator. The 6 x 6 Hamiltonian matrix is derived in a diabatic spin-orbital electronic basis set, including terms up to fourth order in the expansion of the molecular Hamiltonian in the bending normal coordinate about the linear geometry. The symmetry properties of the Hamiltonian are analyzed. Aside from the nonrelativistic fourth-order Renner-Teller vibronic coupling within the (1)Delta state and the second-order nonrelativistic vibronic coupling between the (1)Sigma(+) and (1)Delta states, there exist zeroth-order, first-order, as well as third-order vibronic coupling terms of spin-orbit origin. The latter are absent when the phenomenological expression for the spin-orbit coupling operator is used instead of the microscopic form. The effects of the nonrelativistic and spin-orbit-induced vibronic coupling mechanisms on the (3)Sigma(-), (1)Delta, and (1)Sigma(+) adiabatic potential energy surfaces as well as on the spin-vibronic energy levels are discussed for selected parameter values.     

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.     

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.     

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.     

A theoretical investigation of charge transfer in several substituted acridinium ions

We present calculations for various properties of the ground and excited states of several arylamine-substituted acridinium ion systems that have been studied experimentally. Using ab initio and semiempirical quantum mechanical methods together with the generalized Mulliken-Hush (GMH) model, we examine the excitation energies, dipole moment shifts, and electronic coupling elements for the vertical charge shift (CSh) processes in these systems. We also examine solvent effects on these properties using a dielectric continuum reaction field model. The results are in generally good agreement with available experimental results and indicate that there is strong electronic coupling in these systems over a wide range of torsional angles. Nevetheless, the initial and final cationic states remain reasonably well-localized over this range, and thus TICT state formation is unlikely in these systems. Finally, a version of the GMH model based on Koopmans' Theorem is developed and found to yield coupling elements generally within a factor of 2 of the many-electron GMH for a sample acridinium system, but with overestimated adiabatic and diabatic dipole moment differences.     

Simulation of a complex spectrum: interplay of five electronic states and 21 vibrational degrees of freedom in C5H4 +

Using a five-state, all-mode vibronic coupling model Hamiltonian derived in a previous publication [A. Markmann et al., J. Chem. Phys. 122, 144320 (2005)], we have calculated the photoelectron spectrum of the pentatetraene cation in the neighborhood of the B (2)E state, which can be represented with charge-localized components. To this end, quantum nuclear dynamics calculations were performed using the multiconfiguration time-dependent Hartree method, taking all 21 vibrational normal modes into account. Compared to experiment, the main features are reproduced but higher accuracy experiments are necessary to gauge the accuracy of the predictions for the vibronic progressions at the rising flank of the spectrum.     

Oxidation of cinnamic acid derivatives: A pulse radiolysis and theoretical study

We introduce an algorithm to solve the secular equation that arises in the time independent multimode expansion of the quadratic vibronic coupling problem in parallel. The implementation can handle expansions of arbitrary length, with the open-ended character of the algorithm achieved through the use of fine grained parallelism to partition the trial vectors. The characteristics of the algorithm are discussed and its utility is illustrated by determining a model photoelectron spectrum of the ethoxy radical (C₂H₅O) using a vibronic expansion involving more than 1 billion vibronic basis states. This calculation also represents the first determination of a photoelectron spectrum obtained using a diabatic Hamiltonian obtained with a recently introduced ab initio surface reshaping procedure.     

A time-dependent wave packet study of the vibronic and spin-orbit interactions in the dynamics of Cl((2)P)+H(2)-->HCl(X (1)Sigma(g) (+))+H((2)S) reaction

We investigate the vibronic and spin-orbit (SO) coupling effects in the state-selected dynamics of the title reaction with the aid of a time-dependent wave packet approach. The ab initio potential energy surfaces of Capecchi and Werner [Science 296, 715 (2002)] have been employed for this purpose. Collinear approach of the Cl((2)P) atom to the H(2) molecule splits the degeneracy of the (2)P state and gives rise to (2)Sigma and (2)Pi electronic states. These two surfaces form a conical intersection at this geometry. These states transform as 1 (2)A('), 1 (2)A("), and 2 (2)A('), respectively, at the nonlinear configurations of the nuclei. In addition, the SO interaction due to Cl atom further splits these states into (2)Sigma(1/2), (2)Pi(3/2), and (2)Pi(1/2) components at the linear geometry. The ground-state reagent Cl((2)P(3/2))+H(2) correlates with (2)Sigma(1/2) and (2)Pi(3/2), where as the SO excited reagent Cl(*)((2)P(1/2))+H(2) correlates with (2)Pi(1/2) at the linear geometry. In order to elucidate the impact of the vibronic and SO coupling effects on the initial state-selected reactivity of these electronic states we carry out quantum scattering calculations based on a flux operator formalism and a time-dependent wave packet approach. In this work, total reaction probabilities and the time dependence of electronic population of the system by initiating the reaction on each of the above electronic states are presented. The role of conical intersection alone on the reaction dynamics is investigated with a coupled two-state model and for the total angular momentum J=0 (neglecting the electronic orbital angular momentum) both in a diabatic as well as in the adiabatic electronic representation. The SO interaction is then included and the dynamics is studied with a coupled three-state model comprising six diabatic surfaces for the total angular momentum J=0.5 neglecting the Coriolis Coupling terms of the Hamiltonian. Companion calculations are carried out for the uncoupled adiabatic and diabatic surfaces in order to explicitly reveal the impact of two different surface coupling mechanisms in the dynamics of this prototypical reaction.     

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.     

Spin-orbit vibronic coupling in 3Pi states of linear triatomic molecules

The Renner-Teller vibronic-coupling problem of a 3Pi electronic state of a linear molecule is analyzed with the inclusion of the spin-orbit coupling of the 3Pi electronic state, employing the microscopic (Breit-Pauli) spin-orbit coupling operator for the two unpaired electrons. The 6x6 Hamiltonian matrix in a diabatic spin-electronic basis is obtained by an expansion of the molecular Hamiltonian in powers of the bending amplitude. The symmetry properties of the Hamiltonian with respect to the time-reversal operator and the relativistic vibronic angular momentum operator are analyzed. It is shown that there exists a linear vibronic-coupling term of spin-orbit origin, which has not been considered so far in the Renner-Teller theory of 3Pi electronic states. While two of the six adiabatic electronic wave functions do not exhibit a geometric phase, the other four carry nontrivial topological phases which depend on the radius of the integration contour. The spectroscopic effects of the linear spin-orbit vibronic-coupling mechanism have been analyzed by numerical calculations of the vibronic spectrum for selected model examples.     

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.     

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.     

Systematic corrections to the Born-Oppenheimer approximation

A method for providing systematic diabatic corrections to the Born-Oppenheimer approximation is presented. We begin with an adiabatic expansion of the exact vibronic wavefunctions and, via the molecular Hamiltonian, develop expressions for the diabatic terms in the Schrödinger equation. We then derive recursion relations which allow one to introduce the diabatic interactions to any desired degree of approximation. As an example, the first approximation (beyond the Born-Oppenheimer approximation) is discussed explicitly. In passing, we assess some of the common misconceptions associated with the Born-Oppenheimer approximation.     

Theoretical study of electronically excited radical cations of naphthalene and anthracene as archetypal models for astrophysical observations. Part I. Static aspects

Motivated by the recent discovery of new diffuse interstellar bands and results from laboratory experiments, ab initio quantum chemistry calculations are carried out for the lowest six electronic states of naphthalene and anthracene radical cations. The calculated adiabatic electronic energies are utilized to construct suitable diabatic electronic Hamiltonians in order to perform nuclear dynamics studies in Part II. Complex entanglement of the electronic states is established for both the radical cations and the coupling surfaces among them are also derived in accordance with the symmetry selection rules. Critical examination of the coupling parameters of the Hamiltonian suggests that 29 (out of 48) and 31 (out of 66) vibrational modes are relevant in the nuclear dynamics in the six lowest electronic states of naphthalene and anthracene radical cations, respectively.     

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).