Vibronic Coupling Effects Research Articles

A theoretical study of the chiroptical properties of molecules with isotopically engendered chirality

There has been a considerable interest in the chiroptical properties of molecules whose chirality is exclusively due to an isotopic substitution and numerous examples for the electronic circular dichroism (CD) spectra of isotopically chiral systems have been reported in literature. Four different explanations have been proposed for the mechanism as to how the isotopic substitution induces a chiral perturbation of the otherwise achiral electronic wave function; however, up to now no conclusive answer has been given about the dominating effect responsible for the experimental observations. In this study we will present, for the first time, fully quantum-mechanical calculations of the CD spectra of three different molecular systems with isotopically engendered chirality. As examples, we consider the spectra of organic molecules with ketone and alpha-diketone carbonyl and diene chromophores. The effect of vibronic couplings for the reorientation of the electric and magnetic transition dipole moments is taken into account within the Herzberg-Teller approximation. The ground and excited state geometries and vibrational normal modes are obtained with (time-dependent) density functional theory [(TD)DFT], while the vibronic coupling effects are calculated at the TDDFT and density functional theory/multireference configuration interaction (DFT/MRCI) levels of theory. Generally, the band shapes of the experimental CD spectra are reproduced very well, and also the absolute CD intensities from the simulations are of the right order of magnitude. The sign and the intensity of the CD band are determined by a delicate balance of the contributions of a large number of individual vibronic transitions, and it is found that the vibrational normal modes with a large displacement are dominant. The separation of the calculated CD spectrum into the different contributions due to the overlap of the in-plane and out-of-plane components (regarding the symmetry plane of the unsubstituted molecule) of the electric and magnetic transition dipole moments yields information about the influence of the vibronic coupling effects for the reorientation of the corresponding transition dipole moments. In conclusion, the calculations clearly show that vibronic effects are responsible or at least dominant for the chiroptical properties of isotopically chiral organic molecules.

Charge Transfer through a Protein−Nano Junction

We address the problem of charge transfer (CT) between a nanosized inorganic system and a protein from a theoretical and numerical perspective. The CT process is described on an atomistic level by applying an electronic Hamiltonian that takes into account the chemical bond, vibronic coupling effects, and polarization degrees of freedom. As a structurally well-characterized example, we consider a complex of C60 and its antibody. For this system, we find a novel efficient protein CT mechanism; through-space superexchange is mediated by stacked pi orbital systems. The predicted rates are comparable to those obtained for short-range electron tunneling through covalent bonds, the fastest ground-state CT process known for proteins.

The influence of vibronic coupling on the shape of transport characteristics in inelastic tunneling through molecules

Here, we present theoretical studies of the effect of vibronic coupling on nonlinear transport characteristics (current–voltage and conductance–voltage) in molecular electronic devices. Considered device is composed of molecular quantum dot (with discrete energy levels) weakly connected to metallic electrodes (treated within the wide-band approximation), where molecular vibrations are modeled as dispersionless phonon excitations. Non-perturbative computational scheme, used in this work, is based on the Green's function theory within the framework of mapping technique (GFT–MT) which transforms the many-body electron–phonon interaction problem into a one-body multi-channel single-electron scattering problem. In particular, it is shown that quantum coherent transport of virtual polarons through the molecule can be a dominant factor justifying some well-known discrepancies between theoretical calculations and experimental results.

Characterization of infrared vibrational activity in specific totally symmetric bridging modes of mixed-valence systems near the localized-to-delocalized transition

The presence or absence of infrared (IR) activity in totally symmetric bridging vibrations of ligand-bridged mixed-valence molecular systems has often been taken, on the basis of electronic (a)symmetry arguments, as markers for electronic localization (class II) or delocalization (class III) on the vibrational time scale. However, because IR absorption intensity in such nominally-forbidden modes may be anomalously enhanced due to vibronic coupling effects, especially for cases in the localized-to-delocalized (class II/III) transition regime, a direct and continuous correlation between the extent of (de)localization and IR activity is challenged. In order to experimentally illustrate such phenomena, here we provide a detailed comparison of relevant IR signatures across a series of structurally related, symmetric dinuclear complexes of the type [(bpy) 2(Cl)M-pz-M(Cl)(bpy) 2] n+ (bpy = 2,2′-bipyridine, pz = pyrazine, M = Ru II,III or Os II,III; n = 2, 3, or 4), in which the “mixed valency” (II,III; n = 3) has been characterized as largely localized for M = Ru and approaching the near-delocalized behavior for M = Os. To improve analytical accuracy and facilitate standardization in the comparison of results spanning the various isovalent and mixed-valent redox species, the IR spectroscopic features were probed via an in situ spectroelectrochemical (SEC) approach, in identical medium (solution) conditions. The parent monomers, i.e. [(bpy) 2(Cl)M-pz] n+ (M = Ru II,III or Os II,III; n = 1 or 2), which represent the extreme examples of structural and electronic symmetry breaking in the series, were also investigated and compared with the dimers. In all cases reported here, the spectroscopic assignments of vibrational modes were supported by isotopic modification (deuteration) of the bridging pyrazine ligand.

Pseudo-Jahn-Teller origin of geometry and pseudorotations in second row tetra-atomic clusters X4 (X=Na,Mg,Al,Si,P,S)

Experimentally determined or ab initio calculated molecular geometries carry no information about their origin. Employing the Jahn-Teller (JT) vibronic coupling effects as the only source of instability and consequent distortions of high-symmetry molecular configurations, we have worked out a procedure that allows us to trace the origin of particular geometries and determine the detailed electronic mechanism of their formation. This procedure is illustrated by considering a series of X(4) clusters with X=Na, Mg, Al, Si, P, and S. It shows explicitly why Na(4), Si(4), and Al(4) have a rhombic geometry in the ground state, while Mg(4) and P(4) are tetrahedral, whereas S(4) is a trapezium. Even when the minimum-energy geometries are the same (as in the case of rhombic Na(4), Si(4), and Al(4)), the electronic mechanism of their formation is quite different. In particular, in Na(4) and Si(4) the rhombic minima are produced by a strong pseudo JT coupling between two excited states in the square-planar configuration (different in the two cases) that stabilizes one of them and makes it the ground state by rhombic distortions. The rhombic configuration of Al(4) is due to the pseudo JT effect in its ground-state square-planar configuration, and the trapezium in S(4) is formed by two pseudo JT couplings essentially involving excited states. In several cases this analysis shows also the tunneling paths between equivalent configurations.

Investigation of Herzberg–Teller Franck–Condon approaches and classical simulations to include effects due to vibronic coupling in circular dichroism spectra: The case of dimethyloxirane continued

AbstractA recent study has shown that the inclusion of vibrational effects may be vital in first‐principles simulations of circular dichroism (CD) spectra. In the present work, we show that effects from vibronic coupling or, alternatively, Herzberg–Teller corrections, can have additional and perhaps unusually strong effects, due to delicate cancellations between positive and negative contributions in a CD spectrum. As full vibronic coupling simulations tend to be too demanding computationally for the sizeable molecules considered in CD spectroscopy, it is pertinent to investigate suitable approximations. In the first part of this study, we examine various Herzberg–Teller Franck–Condon (HT–FC) approaches that include the geometrical dependence of the rotatory strength for a 3 × 3 linear vibronic model, for which exact numerical results are easily obtained. Somewhat disappointingly, none of the HT–FC approaches investigated here yielded sufficiently satisfactory results. In a subsequent part of this study, we show that purely classical simulations, based on a vibronic model, can provide reliable spectra and appear to be well suited to address the dependence of the rotatory strength on nuclear geometry. From the classical simulations we extract average rotatory strengths for each electronic state, which are then used in subsequent gradient FC calculations to incorporate vibrational fine structure in the CD spectrum. This mixed classical/gradient FC approach is applied to the methyloxirane CD spectrum, using the statistical averaging of (model) orbital potentials–time‐dependent density functional theory (SAOP–TDDFT) vibronic model presented recently and is shown to improve substantially on the original simulation, corroborating the potential importance of vibronic coupling effects in simulations of CD spectra. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006

Symmetry-Resolved Absorption Spectra of Vibrationally ExcitedCO2Molecules

Symmetry-resolved x-ray absorption spectroscopy has been first carried out on high-temperature molecules. From the angle-resolved ion yield spectra of CO2 both at room temperature and at 430 degrees C, symmetry-resolved absorption profiles of the C 1s(-1) 2pi(u) and O 1s(-1) 2pi(u) resonances have been extracted for the vibrational ground state molecules and bending-vibration excited ones. The profiles change dramatically between them, and the Renner-Teller effect becomes more evident for the vibrationally excited molecules. The effects of the multimode vibronic coupling are suggested for the O 1s(-1) 2pi(u) and O 1s(-1) 3s sigma(g) resonances.

Spectroscopic effects of first-order relativistic vibronic coupling in linear triatomic molecules

It has recently been shown that there exists, in addition to the well-known nonrelativistic Renner-Teller coupling, a linear (that is, of the first order in the bending distortion) vibronic-coupling mechanism of relativistic (that is, spin-orbit) origin in 2II electronic states of linear molecules [L. V. Poluyanov and W. Domcke, Chem. Phys. 301, 111 (2004)]. The generic aspects of the relativistic linear vibronic-coupling mechanism have been analyzed in the present work by numerical calculations of the vibronic spectrum for appropriate models. The vibronic and spin-orbit parameters have been determined by accurate ab initio electronic-structure calculations for the X 2II states of a series of triatomic radicals and radical cations. It is shown for the example of GeCH that the relativistic linear vibronic-coupling mechanism provides a quantitative explanation of the pronounced perturbations in the vibronic spectrum of the X 2II state of GeCH, which previously have been termed "Sears resonances" [S.-G. He, H. Li, T. C. Smith, D. J. Clouthier, and A. J. Merer, J. Chem. Phys. 119, 10115 (2003)]. The X 2II vibronic spectra of the series BS2, CS2+, OCS+, and OBS illustrate the interplay of nonrelativistic and relativistic vibronic-coupling mechanisms in Renner-Teller systems.

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

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.

Allene and pentatetraene cations as models for intramolecular charge transfer: Vibronic coupling Hamiltonian and conical intersections

We consider the vibronic coupling effects involving cationic states with degenerate components that can be represented as charge localized at either end of the short cumulene molecules allene and pentatetraene. Our aim is to simulate dynamically the charge transfer process when one component is artificially depopulated. We model the Jahn-Teller vibronic interaction within these states as well as their pseudo-Jahn-Teller coupling with some neighboring states. For the manifold of these states, we have calculated cross sections of the ab initio adiabatic potential energy surfaces along all nuclear degrees of freedom, including points at large distances from the equilibrium to increase the physical significance of our model. Ab initio calculations for the cationic states of allene and pentatetraene were based on the fourth-order Møller-Plesset method and the outer valence Green's function method. In some cases we had to go beyond this method and use the more involved third-order algebraic diagrammatic construction method to include intersections with satellite states. The parameters for a five-state, all-mode diabatic vibronic coupling model Hamiltonian were least-square fitted to these potentials. The coupling parameters for the diabatic model Hamiltonian are such that, in comparison to allene, an enhanced preference for indirect charge transfer is predicted for pentatetraene.

Effect of magnetic exchange, double exchange, vibronic coupling, and asymmetry on magnetic properties in d2–d3 mixed‐valence dimers

AbstractThe effect of magnetic exchange, double exchange, vibronic coupling, and asymmetry on magnetic properties of d2–d3 systems is discussed. The temperature‐dependent magnetic moment was calculated with the semiclassical adiabatic approach. The results show that the vibronic coupling from the out‐of‐phase breathing vibration on the metal sites (Piepho, Krausz, and Schatz [PKS] model) and the vibronic coupling from the stretching vibration between the metal sites (P model) favor the localization and delocalization of the “extra” electron in mixed‐valence dimers, respectively. The magnetic properties are determined by the interplay among magnetic exchange, double exchange, and vibronic coupling. The results obtained by analyzing d2–d3 systems can be generalized to other full delocalized dinuclear mixed valence systems with a unique transferable electron. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005

On quantifying the vibronic interaction between electronic states

An accurate estimation of the interstate vibronic coupling strength is of particular relevance for the treatment of nonadiabatic dynamics. This is not a trivial task because direct interactions between electronic states have to be separated from intrinsic frequency shifts. Surprisingly, this issue has not been discussed in detail in the literature so far. An analysis of the error dependence is given for two formulas derived from linear vibronic coupling theory. The difficulty in estimating the interstate coupling parameters is shown to originate from the initially unknown contribution of the diagonal quadratic coupling coefficients to the total vibronic coupling. An interpretation of the error analysis including a numerical case study is followed by a more general discussion of the different mechanisms that can shape adiabatic electronic potential energy functions. Qualitative criteria are formulated for the differentiation between interstate and intrastate vibronic coupling effects based on electronic structure information. These ideas are then applied to investigate vibronic coupling problems in pyrazine as well as trans- and cis-hexatriene.

Magnetic properties of d1–d1–d2 MV trimers with partial electron delocalization in the generalized vibronic model

Abstract The effects of magnetic exchange, double exchange and vibronic coupling on magnetic properties of the d1–d1–d2 trimer with C2V symmetry are discussed in the generalized vibronic model. The magnetic moments are calculated with the semiclassical adiabatic approach. The results show that the PKS vibronic coupling and the P vibronic coupling favor the localization and the delocalization of the ‘extra’ electron, respectively. The magnetic properties are determined by the interplay among magnetic exchange, double exchange and vibronic coupling.

Norbornane: An investigation into its valence electronic structure using electron momentum spectroscopy, and density functional and Green’s function theories

We report on the results of an exhaustive study of the valence electronic structure of norbornane (C(7)H(12)), up to binding energies of 29 eV. Experimental electron momentum spectroscopy and theoretical Green's function and density functional theory approaches were all utilized in this investigation. A stringent comparison between the electron momentum spectroscopy and theoretical orbital momentum distributions found that, among all the tested models, the combination of the Becke-Perdew functional and a polarized valence basis set of triple-zeta quality provides the best representation of the electron momentum distributions for all of the 20 valence orbitals of norbornane. This experimentally validated quantum chemistry model was then used to extract some chemically important properties of norbornane. When these calculated properties are compared to corresponding results from other independent measurements, generally good agreement is found. Green's function calculations with the aid of the third-order algebraic diagrammatic construction scheme indicate that the orbital picture of ionization breaks down at binding energies larger than 22.5 eV. Despite this complication, they enable insights within 0.2 eV accuracy into the available ultraviolet photoemission and newly presented (e,2e) ionization spectra, except for the band associated with the 1a(2) (-1) one-hole state, which is probably subject to rather significant vibronic coupling effects, and a band at approximately 25 eV characterized by a momentum distribution of "s-type" symmetry, which Green's function calculations fail to reproduce. We note the vicinity of the vertical double ionization threshold at approximately 26 eV.

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.

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.

Accurate theoretical near-equilibrium potential energy and dipole moment surfaces of HgClO and HgBrO.

The complexes HgBrO and HgClO have been previously determined by ab initio methods to be strongly bound and were suggested to be important intermediates during mercury depletions events observed in the polar troposphere. In the present work accurate near-equilibrium potential energy surfaces (PESs) of these species are reported. The PESs are determined using accurate coupled cluster methods and a series of correlation consistent basis sets with subsequent extrapolation to the complete basis set limit. Additive corrections for both core-valence correlation energy and relativistic effects are also included. The anharmonic ro-vibrational spectra of HgBrO and HgClO have been calculated in variational calculations. Strong infrared band strengths are predicted for all fundamentals in these species. The spin-orbit splitting dominates over the vibronic coupling effect in both HgClO and HgBrO. The Renner-Teller vibronic energy levels corresponding to the bending mode of these molecules are calculated via perturbation theory.

Structural and spectroscopic effects of vibronic coupling in the C 2F radical

The lowest three (1 2A ′,2 2A ′,1 2A ′′) potential energy surfaces of the C 2F radical have been studied at the ab initio level, using Multi Reference Configuration Interaction techniques. For linear geometries, the three surfaces correlate with a 2 Π and a 2 Σ + state, which are very close in energy. Only the X 2A ′ ground state was found to be bent, with R CC=1.271 Å; R CF=1.276 Å; ∠CCF=165°, and a barrier to linearity of 275 cm −1. The spin–rovibronic energy levels up to J=7/2 have been calculated using a recently developed method [Carter et al., Mol. Phys. 98 (2000) 1967]. Almost all of the resulting levels arise from a strong mixture of two out of three electronic states and their assignment is intrinsically ambiguous. A partial characterization, based on the shape of the vibronic wavefunctions, has been made.

The effects of anisotropy in Jahn–Teller systems: application to the icosahedral H ⊗ (h ⊕ g)system

Jahn–Teller (JT) coupling between electronic motion and lattice or molecularvibrations results in an adiabatic potential energy surface that contains eitherwells or troughs of minimum-energy points. When wells are lowest in energy, thesystem will vibrate about the minimum-energy points. This vibration must betaken into account when describing the quantum mechanical states of the system.In general, the wells will be intrinsically anisotropic. This anisotropy alters thevibrational frequencies and hence the positions of the energy levels, and can beparticularly significant when the barriers between wells are shallow. Inthis paper, we will show how anisotropic states and their energies can becalculated using two unitary transformations. The first locates minimaon the adiabatic potential energy surface, and the second accounts foranisotropy in the shape of the minima. The method is developed in away general enough to allow it to be applied to any linear JT problem.The theory is then applied to the icosahedral H ⊗ (h ⊕ g) JTsystem. The results obtained will help the understanding of, for example,the effects of vibronic coupling in positively charged fullerene ions.

Variational calculations of HBN energy levels in the X 2Π and A 2Σ+ states

A theoretical study of the HBN radical in the X 2Π and A 2Σ+ states, taking into account vibronic coupling effects, is reported. The lowest (1 2A′,1 2A″,2 2A′) potential energy surfaces (PES) of the HBN–BNH system have been studied to identify all stationary points. The HBN minimum was found to be 20.0 kcal/mol above BNH, with an isomerization barrier of ≈11 000 cm−1 on the 1 2A′ surface. For the HBN isomer, accurate near-equilibrium three-dimensional diabatic PESs for the ground X 2Π (1 2A′,1 2A″) and first excited A 2Σ+ (2 2A′) electronic states have been calculated at the multireference configuration interaction level of theory, with extended basis set. A vibronic coupling between bend and BN stretch, analogous to that found in the isoelectronic C2H and HCN+ radicals, has been found to take place due to the crossing of the X 2Π and A 2Σ+ states at energies close to 11 000 cm−1. Vibronic energy levels of HBN and DBN have been calculated variationally using a previously developed method [Carter et al., Mol. Phys. 98, 1967 (2000)] suitable for three-atomic molecules showing three-state vibronic interactions. Energy levels of Σ and Π symmetry up to 10 000 cm−1 for HBN, and 8800 cm−1 for DBN, are reported. It is shown that due to the high-energy surface crossing, the vibronic interaction becomes non-negligible only for levels above 8500 cm−1. For all levels, Renner–Teller effects and Fermi resonances are analyzed.