Current Issues in Nonadiabatic Chemistry

Hydroformylation of pyrolysis oils to aldehydes and alcohols from polyolefin waste

Waste plastics are an abundant feedstock for the production of renewable chemicals. Pyrolysis of waste plastics produces pyrolysis oils with high concentrations of olefins (>50 weight %). The traditional petrochemical industry uses several energy-intensive steps to produce olefins from fossil feedstocks such as naphtha, natural gas, and crude oil. In this work, we demonstrate that pyrolysis oil can be used to produce aldehydes through hydroformylation, taking advantage of the olefin functionality. These aldehydes can then be reduced to mono- and dialcohols, oxidized to mono- and dicarboxylic acids, or aminated to mono- and diamines by using homogeneous and heterogeneous catalysis. This route produces high-value oxygenated chemicals from low-value postconsumer recycled polyethylene. We project that the chemicals produced by this route could lower greenhouse gas emissions ~60% compared with their production through petroleum feedstocks.

From a one-mode to a multi-mode understanding of conical intersection mediated ultrafast organic photochemical reactions

This review discusses how ultrafast organic photochemical reactions are controlled by conical intersections, highlighting that decay to the ground-state at multiple points of the intersection space results in their multi-mode character.

Variational Squeezed Davydov Ansatz for Realistic Chemical Systems with Nonlinear Vibronic Coupling

Chemical systems normally possess strong nonlinear vibronic couplings at both zero and finite temperature. For the lowest-order quadratic couplings, here, we introduce a squeezing operator into a variational coherent-state-based method, Davydov ansatz, to simulate the quantum dynamics and the respective spectroscopy. Two molecular systems, pyrazine and the 2-pyridone dimer, are taken as calculated model systems, both of which involve nontrivial quadratic vibronic couplings in high- and low-frequency regions, respectively. Upon a comparison with the benchmarks, the method manifests its advantage for nonlinear couplings. The squeezed bases are also proven to be applicable for the finite temperature by adapting with the thermofield dynamics.

Electronic Structure Methods for the Description of Nonadiabatic Effects and Conical Intersections

Nonadiabatic effects are ubiquitous in photophysics and photochemistry, and therefore, many theoretical developments have been made to properly describe them. Conical intersections are central in nonadiabatic processes, as they promote efficient and ultrafast nonadiabatic transitions between electronic states. A proper theoretical description requires developments in electronic structure and specifically in methods that describe conical intersections between states and nonadiabatic coupling terms. This review focuses on the electronic structure aspects of nonadiabatic processes. We discuss the requirements of electronic structure methods to describe conical intersections and nonadiabatic couplings, how the most common excited state methods perform in describing these effects, and what the recent developments are in expanding the methodology and implementing nonadiabatic couplings.

Rotational and fine structure of open-shell molecules in nearly degenerate electronic states. II. Interpretation of experimentally determined interstate coupling parameters of alkoxy radicals

Rotationally and fine-structure resolved B̃←X̃ laser-induced fluorescence (LIF) spectra of alkoxy radicals have been simulated with a "coupled two-states model" [J. Liu, J. Chem. Phys. 148, 124112 (2018)], in which the nearly degenerate X̃ and à states are considered together. These two electronic states are separated by the "difference potential" and coupled by the spin-orbit (SO) interaction and the Coriolis interaction. Molecular constants determined in fitting the LIF spectra using the coupled two-states model provide quantitative insight into the SO and Coriolis interactions, as well as other intramolecular dynamics, including the pseudo-Jahn-Teller effect. The spectroscopic model also allows semi-quantitative prediction of effective spin-rotation constants using molecular geometry and SO constants, which can be calculated ab initio with considerable accuracy. The dependence of fit values of molecular constants on the size and conformation of alkoxy radicals is discussed.

Extending nudged elastic band method to reaction pathways involving multiple spin states

There are diverse reactions including spin-state crossing, especially the reactions catalyzed by transition metal compounds. To figure out the mechanisms of such reactions, the discussion of minimum energy intersystem crossing (MEISC) points cannot be avoided. These points may be the bottleneck of the reaction or inversely accelerate the reactions by providing a better pathway. It is of great importance to reveal their role in the reactions by computationally locating the position of the MEISC points together with the reaction pathway. However, providing a proper initial guess for the structure of the MEISC point is not as easy as that of the transition state. In this work, we extended the nudged elastic band (NEB) method for multiple spin systems, which is named the multiple spin-state NEB method, and it is successfully applied to find the MEISC points while optimizing the reaction pathway. For more precisely locating the MEISC point, a revised approach was adopted. Meanwhile, our examples also suggest that special attention should be paid to the criterion to define an image optimized as the MEISC point.

A Robust and Unified Solution for Choosing the Phases of Adiabatic States as a Function of Geometry: Extending Parallel Transport Concepts to the Cases of Trivial and Near-Trivial Crossings

We investigate a simple and robust scheme for choosing the phases of adiabatic electronic states smoothly (as a function of geometry) so as to maximize the performance of ab initio non-adiabatic dynamics methods. Our approach is based upon consideration of the overlap matrix (U) between basis functions at successive points in time and selecting the phases so as to minimize the matrix norm of log(U). In so doing, one can extend the concept of parallel transport to cases with sharp curve crossings. We demonstrate that this algorithm performs well under extreme situations where dozens of states cross each other either through trivial crossings (where there is zero effective diabatic coupling), or through non-trivial crossings (when there is a non-zero diabatic coupling), or through a combination of both. In all cases, we compute the time-derivative coupling matrix elements (or equivalently non-adiabatic derivative coupling matrix elements) that are as smooth as possible. Our results should be of interest to all who are interested in either non-adiabatic dynamics, or more generally, parallel transport in large systems.

Probing photodissociation dynamics using ring polymer molecular dynamics

The performance of the ring polymer molecular dynamics (RPMD) approach to simulate typical photodissociation processes is assessed. The correct description of photodissociation requires the calculation of correlation functions or expectation values associated with non-equilibrium initial conditions, which was shown to be possible with RPMD very recently [J. Chem. Phys. 145, 204118 (2016)]. This approach is combined with treatment of the nonadiabatic dynamics employing the ring polymer surface hopping approach (RPSH), which is based on Tully's fewest switches surface hopping (FSSH) approach. The performance is tested using one-dimensional photodissociation models. It is found that RPSH with non-equilibrium initial conditions can well reproduce the time-dependent dissociation probability, and adiabatic and diabatic populations for cases where the crossing point is below and above the Franck-Condon point, respectively, while standard FSSH fails to reproduce the exact quantum dynamics in the latter case. Thus, it is shown that RPSH is an efficient and accurate alternative to standard FSSH, which is one of the most widely employed approaches to study photochemistry.

Atomistic Simulation of Adiabatic Reactive Processes Based on Multi-State Potential Energy Surfaces

The adiabatic reactive molecular dynamics (ARMD) method provides a framework to study chemical reactions using molecular dynamics simulations with minimal computational overhead. Here, ARMD is generalized to an arbitrary reactive process between two states in which reactants and products can be treated by an atomistic force field. The implementation is described, and the method is applied to two systems: the kinetics of NO rebinding to myoglobin (Mb) as a validation system and the conformational transition in neuroglobin (Ngb) which explores the full functionality of ARMD. For MbNO, the nonexponential kinetics observed both in experiment and earlier ARMD studies is reproduced. Furthermore, the sensitivity of the results with respect to the asymptotic separation between the two potential energy surfaces (NO bound and unbound) is studied.

A finite-element visualization of quantum reactive scattering. II. Nonadiabaticity on coupled potential energy surfaces

This is the second in a series of papers detailing a MATLAB based implementation of the finite element method applied to collinear triatomic reactions. Here, we extend our previous work to reactions on coupled potential energy surfaces. The divergence of the probability current density field associated with the two electronically adiabatic states allows us to visualize in a novel way where and how nonadiabaticity occurs. A two-dimensional investigation gives additional insight into nonadiabaticity beyond standard one-dimensional models. We study the F((2)P) + HCl and F((2)P) + H2 reactions as model applications. Our publicly available code (http://www2.chem.umd.edu/groups/alexander/FEM) is general and easy to use.

Theoretical study on the mechanism of selective fluorination of aromatic compounds with Selectfluor

The selective fluorination of aromatic compounds with Selectfluor has been studied theoretically. Our calculations indicate that the fluorine bond contributes to the stabilization of the π complexes, and the SET mechanism is preferred over the S_N2 mechanism.

Non-adiabatic dynamics close to conical intersections and the surface hopping perspective

Conical intersections play a major role in the current understanding of electronic de-excitation in polyatomic molecules, and thus in the description of photochemistry and photophysics of molecular systems. This article reviews aspects of the basic theory underlying the description of non-adiabatic transitions at conical intersections, with particular emphasis on the important case when the dynamics of the nuclei are treated classically. Within this classical nuclear motion framework, the main aspects of the surface hopping methodology in the conical intersection context are presented. The emerging picture from this treatment is that of electronic transitions around conical intersections dominated by the interplay of the nuclear velocity and the derivative non-adiabatic coupling vector field.

Dynamical Outcomes of Quenching: Reflections on a Conical Intersection

This review focuses on experimental studies of the dynamical outcomes following collisional quenching of electronically excited OH A2Σ+ radicals by molecular partners. The experimental observables include the branching between reactive and nonreactive decay channels, kinetic energy release, and quantum state distributions of the products. Complementary theoretical investigations reveal regions of strong nonadiabatic coupling, known as conical intersections, which facilitate the quenching process. The dynamical outcomes observed experimentally are connected to the local forces and geometric properties of the nuclei in the conical intersection region. Dynamical calculations for the benchmark OH-H2 system are in good accord with experimental observations, demonstrating that the outcomes reflect the strong coupling in the conical intersection region as the system evolves from the excited electronic state to quenched products.

Spin-flip reactions of Zr + C2H6 researched by relativistic density functional theory

Density functional theory (DFT) with relativistic corrections of zero-order regular approximation (ZORA) has been applied to explore the reaction mechanisms of ethane dehydrogenation by Zr atom with triplet and singlet spin-states. Among the complicated minimum energy reaction path, the available states involves three transition states (TS), and four stationary states (1) to (4) and one intersystem crossing with spin-flip (marked by -->): (3) Zr + C 2 H 6 → (3) Zr-CH 3 -CH 3 ((3)1) → (3)TS 1/2 → (3) ZrH-CH 2 -CH 3 ((3)2) → (3) TS 2/3 --> (1) ZrH2-CH2 = CH2 ((1) 3) → (1) TS 3/4 → (1) ZrH 3 -CH = CH 2 ((1)4). The minimum energy crossing point is determined with the help of the DFT fractional-occupation-number (FON) approach. The spin inversion leads the reaction pathway transferring from the triplet potential energy surface (PES) to the singlet's accompanying with the activation of the second C-H bond. The overall reaction is calculated to be exothermic by about 231 kJ mol(-1). Frequency and NBO analysis are also applied to confirm with the experimental observed data.

Conical intersections in solution: formulation, algorithm, and implementation with combined quantum mechanics/molecular mechanics method

The significance of conical intersections in photophysics, photochemistry, and photodissociation of polyatomic molecules in gas phase has been demonstrated by numerous experimental and theoretical studies. Optimization of conical intersections of small- and medium-size molecules in gas phase has currently become a routine optimization process, as it has been implemented in many electronic structure packages. However, optimization of conical intersections of small- and medium-size molecules in solution or macromolecules remains inefficient, even poorly defined, due to large number of degrees of freedom and costly evaluations of gradient difference and nonadiabatic coupling vectors. In this work, based on the sequential quantum mechanics and molecular mechanics (QM/MM) and QM/MM-minimum free energy path methods, we have designed two conical intersection optimization methods for small- and medium-size molecules in solution or macromolecules. The first one is sequential QM conical intersection optimization and MM minimization for potential energy surfaces; the second one is sequential QM conical intersection optimization and MM sampling for potential of mean force surfaces, i.e., free energy surfaces. In such methods, the region where electronic structures change remarkably is placed into the QM subsystem, while the rest of the system is placed into the MM subsystem; thus, dimensionalities of gradient difference and nonadiabatic coupling vectors are decreased due to the relatively small QM subsystem. Furthermore, in comparison with the concurrent optimization scheme, sequential QM conical intersection optimization and MM minimization or sampling reduce the number of evaluations of gradient difference and nonadiabatic coupling vectors because these vectors need to be calculated only when the QM subsystem moves, independent of the MM minimization or sampling. Taken together, costly evaluations of gradient difference and nonadiabatic coupling vectors in solution or macromolecules can be reduced significantly. Test optimizations of conical intersections of cyclopropanone and acetaldehyde in aqueous solution have been carried out successfully.

Gas-phase fragmentation of deprotonated p-hydroxyphenacyl derivatives

Electrospray ionization of methanolic solutions of p-hydroxyphenacyl derivatives HO-C(6)H(4)-C(O)-CH(2)-X (X = leaving group) provides abundant signals for the deprotonated species which are assigned to the corresponding phenolate anions (-)O-C(6)H(4)-C(O)-CH(2)-X. Upon collisional activation in the gas phase, these anions inter alia undergo loss of a neutral "C(8)H(6)O(2)" species concomitant with formation of the corresponding anions X(-). The energies required for the loss of the neutral roughly correlate with the gas phase acidities of the conjugate acids (HX). Extensive theoretical studies performed for X = CF(3)COO in order to reveal the energetically most favorable pathway for the formation of neutral "C(8)H(6)O(2)" suggest three different routes of similar energy demands, involving a spirocyclopropanone, epoxide formation, and a diradical, respectively.

Stark field control of nonadiabatic dynamics in triatomic hydrogen

We show experimentally that an external electric field can be used to control the amplitudes of nonadiabatic paths taken by a dissociating molecule. In the example presented here, this control is achieved by Stark-field mixing in H(3) Rydberg states with different decay paths. The final state continuum is in each path formed by three-particle wave packets of slow neutral hydrogen atoms in their electronic ground state. Their momentum vector correlations show signs of interference, since the molecule can access the identical continuum via two distinctly different paths, involving different nonadiabatic coupling mechanisms. As an added feature a preferred alignment of the fragmentation plane in the laboratory frame emerges, corresponding to a selective dissociation of molecules oriented along the field direction.

CH4 activation by W atom in the gas phase: a case of two-state reactivity process

Gas-phase methane activation by tungsten (W) atoms was studied at the density functional level of theory using the hybrid exchange correlation functional B3LYP. Four reaction profiles corresponding to the septet, quintet, triplet, and singlet multiplicities were investigated in order to ascertain the presence of some spin inversion during the methane activation. Methane activation mediated by W atoms was found to be a spin-forbidden process resulting from the crossing among the multistate energetic profiles. On the basis of the Hammond postulate, this is a typical two-state reactivity (TSR) reaction. The minimum energy crossing points lead to decrease in the barrier heights of TS01, TS12, TS23, and TS24 that correspond to the first, second, and third hydrogen transfer and the reductive elimination step of H(2), respectively. The spin-orbit coupling is calculated between electronic states of different multiplicities at the crossing points (MECPs) to estimate the intersystem crossing probabilities, and the probability of hopping from one surface to the other in the vicinity of the crossing region is calculated by the Landau-Zener type model.

Topological analysis of the reaction of uranium ions (U+, U2+) with N2O in the gas phase

Density functional theory calculations were performed to study the ability of uranium cations, U(+) and U(2+), to activate the N-N and N-O bonds of N(2)O. A close description of the reaction pathways leading to different reaction products is presented. The obtained results are compared with previous experimental works. The nature of the bonding of all the involved species and the bonding evolution along the reaction pathways was studied by means of the topological analysis of the ELF function.