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.     

Conical intersections of three electronic states affect the ground state of radical species with little or no symmetry: pyrazolyl

Conical intersections of three states of the same symmetry are located in the pyrazolyl radical using wave functions of approximately 40 million configuration state functions. The three-state intersection is found to be only approximately 3400 cm-1 above the minimum energy structure on the ground electronic state. It is suggested that many organic radicals may also exhibit this feature.     

A criterion for the confluence of two seams of conical intersection in triatomic molecules

It is shown that the cross product t ^{I J} (R _x )≡g ^{I J} (R _x )×h ^{I J} (R _x ), where g _τ ^{I J} (R)=(c ^I (R _x )−c ^J (c ^I (R _x )+c ^J (R _x )), h _τ ^{I J} (R)=c ^I (R _x )^† c ^J (R _x ), τ is an internal nuclear coordinate, the c ^I (R) satisfy [H(R)−E _I (R)]c ^I (R)=0 and H(R) is the electronic Hamiltonian matrix, is a unique property of a conical intersection at R _x . t ^{I J} (R _x )=0 when R _x is located at the intersection of two (or more) seams of conical intersection. This criterion for an intersection of two seams of conical intersection has important implications for algorithms that seek to locate such points. Here it␣is␣used to analyze the trifurcation of a generic C_2v ^2S+1 A−^2S+1 B seam of conical intersection, analogous to those recently found in AlH₂ and CH₂. Received: 31 July 1997 / Accepted: 27 August 1997     

A method to reduce the size of the vibronic basis employed in the simulation of spectra using the multimode vibronic coupling approximation

In the time-independent multimode approach for the determination of vibronic spectra involving strongly coupled electronic states, the equilibrium geometry and normal modes of the reference or precursor state are usually employed as the basis for the multimode expansion. This basis, while easily constructed, is generally ill-suited for determining the eigenstates of the observed species. Employing a more computationally effective basis requires the evaluation of Franck-Condon overlap integrals. Using established generalized Hermite polynomial generating function formalisms, an algorithm is developed that can efficiently determine the enormous requisite number of these overlap integrals. It is found that this flexibility in the choice of multimode basis can significantly reduce the size of the basis needed to obtain converged spectral simulations. The previously reported spectrum of the ethoxy (C(2)H(5)O) radical serves as an example of the efficacy of the new technique.     

Relation between electronic structure and the chemiluminescence arising from collisions between alkaline earth atoms and halogen molecules

The chemiluminescence ascribed by Jonah and Zare to radiative association of Ba and Cl₂ is examined in the light of the electronic structure of the ground and excited states of alkaline earth dihalides. A simple discussion is first given in terms of the possible curve crossings and avoided crossings. In addition ab initio self-consistent-field calculations are reported for CaF₂ using an extended basis set. The ¹ B ₂ excited state, from which the molecule may radiate to the ground state, is predicted to have an equilibrium bond angle of 54° and bond distance of 4·06 bohr. The bertical excitation energy to the ¹ B ₂ state is 7·3 eV and the vertical energy difference (¹ A ₁-¹ B ₂) at the ¹ B ₂ equilibrium geometry is 1·3 eV. These results appear consistent with the model proposed by Jonah and Zare. In addition, a variety of properties (dipole moments, field gradients, etc). of CaF₂ are reported.     

On the representation of coupled adiabatic potential energy surfaces using quasi-diabatic Hamiltonians: a distributed origins expansion approach

In two previous papers we have introduced a method to generate coupled quasi-diabatic Hamiltonians (H(d)) that are capable of representing adiabatic energies, energy gradients, and derivative couplings over a wide range of geometries including seams of conical intersection. In this work, two new synergistic features are introduced. Firstly, the functional form of H(d) is generalized. Rather than requiring there to be a low energy point of high symmetry to serve as the unique origin, functions centered on points distributed in nuclear coordinate space are used in the polynomials that comprise the matrix elements in H(d). The use of functions with distributed origins, allows reproduction of the ab initio data with lower order expansions, and offers the possibility of describing multichannel dissociation. The fitting algorithm is combined with a three-step procedure in which the domain of H(d) is extended from a core set of nuclear configurations to a region of nuclear coordinate space appropriate for nuclear dynamics, with a prescribed accuracy. This significant extension of the domain of definition compared to our original work, which is facilitated by the distributed origin approach, is achieved largely through the use of surface hopping trajectories. The 1,2(1)A states of NH(3), which provide an archetypical example of nonadiabatic dynamics, are used to demonstrate the utility of this approach. The representation describes 21 points on the 1(1)A-2(1)A seam of conical intersection and their local topography flawlessly and on the entire domain, the electronic structure data is represented to an accuracy of 77.00 (46.90) cm(-1), as measured by the root mean square (mean unsigned) error for energies lower than 50 000 cm(-1). This error is a factor of 10 lower than that of the most accurate representation of high quality ab initio data, on a comparable domain, previously reported for this system.     

On the determination of partial differential cross sections for photodetachment and photoionization processes producing polyatomic molecules with electronic states coupled by conical intersections

A formalism is derived for the computation of partial differential cross sections for electron photodetachment and photoionization processes that leave the residual or target molecule in electronic states that are strongly coupled by conical intersections. Because the electronic states of the target are nonadiabatically coupled, the standard adiabatic states approach of solving the electronic Schro?dinger equation for the detached electron at fixed nuclear geometries and then vibrationally averaging must be fundamentally modified. We use a Lippmann-Schwinger equation based approach, which leads naturally to a partitioning of the transition amplitude into a Dyson orbital like part plus a scattering correction. The requisite Green's function is that developed in our previous paper for the direct determination of total integral cross sections. The method takes proper account of electron exchange, possible nonorthogonality of the orbital describing the detached electron, and nonadiabatic effects in the product molecule. The Green's function is constructed in an L(2) basis using complex scaling techniques. The accurate treatment of nonadiabatic effects in the residual molecule is accomplished using the multimode vibronic coupling model. For photodetachment, an approximate approach, which is less computationally demanding, is suggested.     

On the simulation of photoelectron spectra complicated by conical intersections: higher-order effects and hot bands in the photoelectron spectrum of triazolide (CH)2N3(-)

We report simulated photoelectron spectra for 1,2,3-triazolide (CH)(2)N(3)(-), which reveal the vibronic energy levels of the neutral radical 1,2,3-triazolyl, (CH)(2)N(3). The spectral simulation using a quasidiabatic Hamiltonian H(d) comprised of polynomials through 4th order (thereby extending conventional quadratic expansions), is compared to both the experimental spectrum and a standard Franck-Condon (adiabatic) simulation. The quartic H(d) is far superior to the quadratic H(d), reproducing the main features of the experimental spectrum and allowing for their subsequent assignment. The contributions from excited anion states successfully reproduce the observed vibronic transitions to the red of the assigned band origin of the neutral species. The algorithmic extensions required for the determination of these hot band contributions to the total spectrum are discussed. Convergence of the spectral envelope with respect to the vibronic basis, including both the principal and hot bands, required more than 10(9) terms.     

Analytic evaluation of nonadiabatic coupling terms at the MR-CI level. I. Formalism

An efficient and general method for the analytic computation of the nonandiabatic coupling vector at the multireference configuration interaction (MR-CI) level is presented. This method is based on a previously developed formalism for analytic MR-CI gradients adapted to the use for the computation of nonadiabatic coupling terms. As was the case for the analytic energy gradients, very general, separate choices of invariant orbital subspaces at the multiconfiguration self-consistent field and MR-CI levels are possible, allowing flexible selections of MR-CI wave functions. The computational cost for the calculation of the nonadiabatic coupling vector at the MR-CI level is far below the cost for the energy calculation. In this paper the formalism of the method is presented and in the following paper [Dallos et al., J. Chem. Phys. 120, 7330 (2004)] applications concerning the optimization of minima on the crossing seam are described.     

Exploring molecular complexity: conical intersections and NH3 photodissociation

The role of conical intersections in the photodissociation of the A 1A2" state of NH3 is investigated using extended atomic basis sets and a configuration state function expansion of approximately 8.5 million terms. A previously unknown portion of the 1 1A-2 1A seam of conical intersections with only C(s) symmetry is located. This portion of the seam is readily accessible from the equilibrium geometry of the A 1A2" state. These conical intersections are expected to play a role in the competition between adiabatic and nonadiabatic pathways for NH3(A 1A2") photodissociation.