Nonadiabatic Reactive Quenching of OH(A2Σ+) by H2: Origin of High Vibrational Excitation in the H2O Product.

The nonadiabatic dynamics of the reactive quenching channel of the OH(A2Σ+) + H2/D2 collisions is investigated with a semiclassical surface hopping method, using a recently developed four-state diabatic potential energy matrix (DPEM). In agreement with experimental observations, the H2O/HOD products are found to have significant vibrational excitation. Using a Gaussian binning method, the H2O vibrational state distribution is determined. The preferential energy disposal into the product vibrational modes is rationalized by an extended Sudden Vector Projection model, in which the h and g vectors associated with the conical intersection are found to have large projections with the product normal modes. However, our calculations did not find significant insertion trajectories, suggesting the need for further improvement of the DPEM.

Nuclear-electronic orbital approach to quantization of protons in periodic electronic structure calculations.

The nuclear-electronic orbital (NEO) method is a well-established approach for treating nuclei quantum mechanically in molecular systems beyond the usual Born-Oppenheimer approximation. In this work, we present a strategy to implement the NEO method for periodic electronic structure calculations, particularly focused on multicomponent density functional theory (DFT). The NEO-DFT method is implemented in an all-electron electronic structure code, FHI-aims, using a combination of analytical and numerical integration techniques as well as a resolution of the identity scheme to enhance computational efficiency. After validating this implementation, proof-of-concept applications are presented to illustrate the effects of quantized protons on the physical properties of extended systems, such as two-dimensional materials and liquid-semiconductor interfaces. Specifically, periodic NEO-DFT calculations are performed for a trans-polyacetylene chain, a hydrogen boride sheet, and a titanium oxide-water interface. The zero-point energy effects of the protons as well as electron-proton correlation are shown to noticeably impact the density of states and band structures for these systems. These developments provide a foundation for the application of multicomponent DFT to a wide range of other extended condensed matter systems.

Up to a Sign. The Insidious Effects of Energetically Inaccessible Conical Intersections on Unimolecular Reactions.

It is now well established that conical intersections play an essential role in nonadiabatic radiationless decay where their double-cone topography causes them to act as efficient funnels channeling wave packets from the upper to the lower adiabatic state. Until recently, little attention was paid to the effect of conical intersections on dynamics on the lower state, particularly when the total energy involved is significantly below that of the conical intersection seam. This energetic deficiency is routinely used as a sufficient condition to exclude consideration of excited states in ground state dynamics. In this account, we show that, this energy criterion notwithstanding, energy inaccessible conical intersections can and do exert significant influence on lower state dynamics. The origin of this influence is the geometric phase, a signature property of conical intersections, which is the fact that the real-valued electronic wave function changes sign when transported along a loop containing a conical intersection, making the wave function double-valued. This geometric phase is permitted by an often neglected property of the real-valued adiabatic electronic wave function; namely, it is determined only up to an overall sign. Noting that in order to change sign a normalized, continuous function must go through zero, for loops of ever decreasing radii, demonstrating the need for an electronic degeneracy (intersection) to accompany the geometric phase. Since the total wave function must be single-valued a compensating geometry dependent phase needs to be included in the total electronic-nuclear wave function. This Account focuses on how this consequence of the geometric phase can modify nuclear dynamics energetically restricted to the lower state, including tunneling dynamics, in directly measurable ways, including significantly altering tunneling lifetimes, thus confounding the relation between measured lifetimes and barrier heights and widths, and/or completely changing product rotational distributions. Some progress has been made in understanding the origin of this effect. It has emerged that for a system where the lower adiabatic potential energy surface exhibits a topography comprised of two saddle points separated by a high energy conical intersection, the effect of the geometric phase can be quite significant. In this case topologically distinct paths through the two adiabatic saddle points may lead to interference. This was pointed out by Mead and Truhlar almost 50 years ago and denoted the Molecular Aharonov-Bohm effect. Still, the difficulty in anticipating a significant geometric phase effect in tunneling dynamics due to energetically inaccessible conical intersections leads to the attribute insidious that appears in the title of this Account. Since any theory is only as relevant as the prevalence of the systems it describes, we include in this Account examples of real systems where these effects can be observed. The accuracy of the reviewed calculations is high since we use fully quantum mechanical dynamics and construct the geometric phase using an accurate diabatic state fit of high quality ab initio data, energies, energy gradients, and interstate couplings. It remains for future work to establish the prevalence of this phenomenon and its deleterious effects on the conventional wisdom discussed in this work.

On the nonadiabatic collisional quenching of OH(A) by H2: a four coupled quasi-diabatic state description.

A four-state diabatic potential energy matrix (DPEM), Hd, for the description of the nonadiabatic quenching of OH(A2Σ+) by collisions with H2 is reported. The DPEM is constructed as a fit to adiabatic energies, energy gradients, and derivative couplings obtained exclusively from multireference configuration interaction wave functions. A four-adiabatic-electronic-state representation is used in order to describe all energetically accessible regions of the nuclear coordinate space. Partial permutation-inversion symmetry is incorporated into the representation. The fit is based on electronic structure data at 42 882 points, described by over 1.6 million least squares equations with a root mean square (mean unsigned) error of 178(83) cm-1. Comparison of ab initio and Hd determined minima, saddle points, and energy minimized points on C2v, Cs, C∞v, and C1 (noncoplanar) portions of two conical intersection seams are used to establish the accuracy of the Hd.

Nonadiabatic Dynamics in Photodissociation of Hydroxymethyl in the 32A(3p x) Rydberg State: A Nine-Dimensional Quantum Study.

The nonadiabatic predissociation dynamics of the hydroxymethyl radical (CH2OH) in its 32A(3p x) state is investigated using a nine-dimensional quantum mechanical model based on an ab initio three coupled diabatic state potential energy matrix. The calculated absorption spectrum, which is dominated by predissociative resonances, is in excellent agreement with experiment. The predissociation is facilitated by two conical intersection seams formed between the 32A(3p x) and 22A(3s) states near the Franck-Condon region. The h and g vectors of energy minimized points on these seams are analyzed using the normal modes of the 32A equilibrium structure. The low-lying predissociative resonances have been assigned and their lifetimes are less than 100 fs and moderately mode specific. The absorption spectrum is dominated by a CO vibrational progression, due apparently to the promotion of an electron from the ground state antibonding πCO* orbital to the carbon Rydberg orbital, which effectively increases the C-O bond order.

Signatures of a Conical Intersection in Adiabatic Dissociation on the Ground Electronic State.

Conical intersections are known to cause nonadiabatic transitions, but their effects on adiabatic dynamics are often ignored. Using the overtone-induced dissociation of the hydroxymethyl radical as an example, we demonstrate that ground-state O-H bond rupture is significantly affected by a conical intersection with an electronically excited state along the dissociation path, despite the much lower energy of the dissociating state than that of the conical intersection. In addition to lifetime differences, the geometric phase leads to a different H2CO rotational state distribution compared with that obtained using the standard single-state adiabatic model, which constitutes a signature of the conical intersection.

Multistate, multichannel coupled diabatic state representations of adiabatic states coupled by conical intersections. CH2OH photodissociation.

A coupled diabatic state representation, Hd, of the 1, 2, 3 2A states of CH2OH suitable for the description of the three channel, three state photodissociation process CH2OH(1 2A) + hv → CH2OH(2, 3 2A) → CH2O(X, A) + H, cis-CHOH + H, trans-CHOH + H, is reported. The representation is based on electronic structure data (energies, energy gradients, and derivative couplings) obtained exclusively from multireference configuration interaction single and double excitation wave functions. Diabat shifting is employed to improve the representation's agreement with accurate experimental energetics. A careful analysis of the numerous minima, saddle points, and conical intersection seams is reported. The computed T0(3 2A) ∼ 35 220 cm-1 is in excellent agreement with the experimental estimate of 35 053 cm-1, and the computed channel dissociation energies, D0, for CH2O 9453 (10 160), cis-HCOH 30 310.2 (29 923), and trans-HCOH 28 799 (28 391) cm-1 are in good accord with the measured values given parenthetically. These accurate energetics over a wide range of nuclear configurations strongly support the ability of this Hd to enable quality simulations of nonadiabatic dynamics.

Dynamic mapping of conical intersection seams: A general method for incorporating the geometric phase in adiabatic dynamics in polyatomic systems.

The incorporation of the geometric phase in single-state adiabatic dynamics near a conical intersection (CI) seam has so far been restricted to molecular systems with high symmetry or simple model Hamiltonians. This is due to the fact that the ab initio determined derivative coupling (DC) in a multi-dimensional space is not curl-free, thus making its line integral path dependent. In a recent work [C. L. Malbon et al., J. Chem. Phys. 145, 234111 (2016)], we proposed a new and general approach based on an ab initio determined diabatic representation consisting of only two electronic states, in which the DC is completely removable, so that its line integral is path independent in the simply connected domains that exclude the CI seam. Then with the CIs included, the line integral of the single-valued DC can be used to construct the complex geometry-dependent phase needed to exactly eliminate the double-valued character of the real-valued adiabatic electronic wavefunction. This geometry-dependent phase gives rise to a vector potential which, when included in the adiabatic representation, rigorously accounts for the geometric phase in a system with an arbitrary locus of the CI seam and an arbitrary number of internal coordinates. In this work, we demonstrate this approach in a three-dimensional treatment of the tunneling facilitated dissociation of the S1 state of phenol, which is affected by a Cs symmetry allowed but otherwise accidental seam of CI. Here, since the space is three-dimensional rather than two-dimensional, the seam is a curve rather than a point. The nodal structure of the ground state vibronic wavefunction is shown to map out the seam of CI.

Nonadiabatic photodissociation dynamics of the hydroxymethyl radical via the 22A(3s) Rydberg state: A four-dimensional quantum study.

The quantum mechanical nonadiabatic photodissociation dynamics of the hydroxymethyl (CH2OH) radical in its lowest absorption band is investigated for the first time on a set of coupled diabatic potential energy surfaces determined by accurately fitting a large set of ab initio data. In this two-state approximation, only the ground and first excited states of CH2OH, which are coupled by conical intersections, are included. The reduced-dimensional dynamical model includes the CO stretch, the COH bend, the HCOH torsion, and the O-H dissociation coordinate. The experimentally measured hydrogen atom kinetic energy distribution is satisfactorily reproduced. The calculated product state distribution of the H2CO(X) fragment indicates strong vibrational excitation in the CO stretching mode, resulting from the relatively large difference in the C-O bond length between the ground and excited electronic states of CH2OH due to the photo-induced promotion of an electron from the half-occupied π*CO antibonding orbital to a Rydberg orbital. In addition, the bimodal kinetic energy distribution is confirmed to originate from nonadiabatic transitions near the conical intersection along the O-H dissociation coordinate.

On the incorporation of the geometric phase in general single potential energy surface dynamics: A removable approximation to ab initio data.

For two electronic states coupled by conical intersections, the line integral of the derivative coupling can be used to construct a complex-valued multiplicative phase factor that makes the real-valued adiabatic electronic wave function single-valued, provided that the curl of the derivative coupling is zero. Unfortunately for ab initio determined wave functions, the curl is never rigorously zero. However, when the wave functions are determined from a coupled two diabatic state Hamiltonian Hd (fit to ab initio data), the resulting derivative couplings are by construction curl free, except at points of conical intersection. In this work we focus on a recently introduced diabatization scheme that produces the Hd by fitting ab initio determined energies, energy gradients, and derivative couplings to the corresponding Hd determined quantities in a least squares sense, producing a removable approximation to the ab initio determined derivative coupling. This approach and related numerical issues associated with the nonremovable ab initio derivative couplings are illustrated using a full 33-dimensional representation of phenol photodissociation. The use of this approach to provide a general framework for treating the molecular Aharonov Bohm effect is demonstrated.

An improved quasi-diabatic representation of the 1, 2, 3(1)A coupled adiabatic potential energy surfaces of phenol in the full 33 internal coordinates.

In a recent work we constructed a quasi-diabatic representation, H(d), of the 1, 2, 3(1)A adiabatic states of phenol from high level multireference single and double excitation configuration interaction electronic structure data, energies, energy gradients, and derivative couplings. That H(d) accurately describes surface minima, saddle points, and also regions of strong nonadiabatic interactions, reproducing the locus of conical intersection seams and the coordinate dependence of the derivative couplings. The present work determines the accuracy of H(d) for describing phenol photodissociation. Additionally, we demonstrate that a modest energetic shift of two diabats yields a quantifiably more accurate H(d) compared with experimental energetics. The analysis shows that in favorable circumstances it is possible to use single point energies obtained from the most reliable electronic structure methods available, including methods for which the energy gradients and derivative couplings are not available, to improve the quality of a global representation of several coupled potential energy surfaces. Our data suggest an alternative interpretation of kinetic energy release measurements near λphot ∼ 248 nm.

Nonadiabatic Photodissociation of the Hydroxymethyl Radical from the 2(2)A State. Surface Hopping Simulations Based on a Full Nine-Dimensional Representation of the 1,2,3(2)A Potential Energy Surfaces Coupled by Conical Intersections.

The nonadiabatic photodissociation CH2OH(1(2)A) + hv → CH2OH(2,3(2)A) → CH2O + H or HCOH(cis or trans) + H is addressed using trajectory surface hopping dynamics on a quasi-diabatic representation, H(d), of the 1,2,3(2)A coupled, adiabatic potential energy surfaces. We focus on dynamics originating on the 2(2)A potential energy surface. The H(d) is based exclusively on electronic structure data obtained from a multireference configuration interaction single and double excitation expansion, composed of over 67 million configuration state functions, and treats all nine internal degrees of freedom in an even-handed manner. Each simulation is based on bundles of 10000 trajectories randomly selected from harmonic Wigner distributions and propagated for up to 1 ps. The bimodal distribution in the kinetic energy release spectrum is explained in terms of direct versus quasi-statistical dissociation.

Full-dimensional quantum stereodynamics of the non-adiabatic quenching of OH(A2Σ+) by H2.

The Born-Oppenheimer approximation, assuming separable nuclear and electronic motion, is widely adopted for characterizing chemical reactions in a single electronic state. However, the breakdown of the Born-Oppenheimer approximation is omnipresent in chemistry, and a detailed understanding of the non-adiabatic dynamics is still incomplete. Here we investigate the non-adiabatic quenching of electronically excited OH(A2Σ+) molecules by H2 molecules using full-dimensional quantum dynamics calculations for zero total nuclear angular momentum using a high-quality diabatic-potential-energy matrix. Good agreement with experimental observations is found for the OH(X2Π) ro-vibrational distribution, and the non-adiabatic dynamics are shown to be controlled by stereodynamics, namely the relative orientation of the two reactants. The uncovering of a major (in)elastic channel, neglected in a previous analysis but confirmed by a recent experiment, resolves a long-standing experiment-theory disagreement concerning the branching ratio of the two electronic quenching channels.

Insights into the Mechanism of Nonadiabatic Photodissociation from Product Vibrational Distributions. The Remarkable Case of Phenol.

The fate of a photoexcited molecule is often strongly influenced by electronic degeneracies, such as conical intersections, which break the Born-Oppenheimer separation of electronic and nuclear motion. Detailed information concerning internal energy redistribution in a nonadiabatic process can be extracted from the product state distribution of a photofragment in photodissociation. Here, we focus on the nonadiabatic photodissociation of phenol and discuss the internal excitation of the phenoxyl fragment using both symmetry analysis and wave packet dynamics. It is shown that unique and general selection rules exist, which can be attributed to the geometric phase in the adiabatic representation. Further, our results provide a reinterpretation of the experimental data, shedding light on the impact of conical intersections on the product state distribution.

Encoding of vinylidene isomerization in its anion photoelectron spectrum.

Vinylidene-acetylene isomerization is the prototypical example of a 1,2-hydrogen shift, one of the most important classes of isomerization reactions in organic chemistry. This reaction was investigated with quantum state specificity by high-resolution photoelectron spectroscopy of the vinylidene anions H2CC- and D2CC- and quantum dynamics calculations. Peaks in the photoelectron spectra are considerably narrower than in previous work and reveal subtleties in the isomerization dynamics of neutral vinylidene, as well as vibronic coupling with an excited state of vinylidene. Comparison with theory permits assignment of most spectral features to eigenstates dominated by vinylidene character. However, excitation of the ν6 in-plane rocking mode in H2CC results in appreciable tunneling-facilitated mixing with highly vibrationally excited states of acetylene, leading to broadening and/or spectral fine structure that is largely suppressed for analogous vibrational levels of D2CC.