Femtochemistry of trans-azomethane: a combined experimental and theoretical study

Semiclassical Nonadiabatic Molecular Dynamics Using Linearized Pair-Density Functional Theory

Nonadiabatic molecular dynamics is an effective method for modeling nonradiative decay in electronically excited molecules. Its accuracy depends strongly on the quality of the potential energy surfaces, and its affordability for long direct-dynamic simulations with adequate ensemble averaging depends strongly on the cost of the required electronic structure calculations. Linearized pair-density functional theory (L-PDFT) is a recently developed post-self-consistent-field multireference method that can model potential energy surfaces with an accuracy similar to expensive multireference perturbation theories but at a computational cost similar to the underlying multiconfiguration self-consistent field method. Here, we integrate the SHARC dynamics and PySCF electronic structure code to utilize L-PDFT for electronically nonadiabatic calculations and use the combined programs to study the photoisomerization reaction of cis-azomethane. We show that L-PDFT is able to successfully simulate the photoisomerization without crashes, and it yields results similar to the more expensive extended multistate complete active space second-order perturbation theory. This shows that L-PDFT can model internal conversion, and it demonstrates its promise for broader photodynamics applications.

Ab Initio Molecular Cavity Quantum Electrodynamics Simulations Using Machine Learning Models

We present a mixed quantum-classical simulation of polariton dynamics for molecule-cavity hybrid systems. In particular, we treat the coupled electronic-photonic degrees of freedom (DOFs) as the quantum subsystem and the nuclear DOFs as the classical subsystem and use the trajectory surface hopping approach to simulate non-adiabatic dynamics among the polariton states due to the coupled motion of nuclei. We use the accurate nuclear gradient expression derived from the Pauli-Fierz quantum electrodynamics Hamiltonian without making further approximations. The energies, gradients, and derivative couplings of the molecular systems are obtained from the on-the-fly simulations at the level of complete active space self-consistent field (CASSCF), which are used to compute the polariton energies and nuclear gradients. The derivatives of dipoles are also necessary ingredients in the polariton nuclear gradient expression but are often not readily available in electronic structure methods. To address this challenge, we use a machine learning model with the Kernel ridge regression method to construct the dipoles and further obtain their derivatives, at the same level as the CASSCF theory. The cavity loss process is modeled with the Lindblad jump superoperator on the reduced density of the electronic-photonic quantum subsystem. We investigate the azomethane molecule and its photoinduced isomerization dynamics inside the cavity. Our results show the accuracy of the machine-learned dipoles and their usage in simulating polariton dynamics. Our polariton dynamics results also demonstrate the isomerization reaction of azomethane can be effectively tuned by coupling to an optical cavity and by changing the light-matter coupling strength and the cavity loss rate.

Ultrafast Internal Conversion Dynamics through the on-the-Fly Simulation of Transient Absorption Pump-Probe Spectra with Different Electronic Structure Methods

An on-the-fly surface-hopping simulation protocol is developed for the evaluation of transient absorption (TA) pump-probe (PP) signals of molecular systems exhibiting internal conversion to the electronic ground state. We study the nonadiabatic dynamics of azomethane and the associating TA PP spectra at three levels of the electronic-structure theory, OM2/MRCI, SA-CASSCF, and XMS-CASPT2. The impact of these methods on the population dynamics and time-resolved TA PP signals is substantially different. This difference is attributed to the strong non-Condon effects that must be taken into account for the proper understanding and interpretation of time-resolved TA PP signals of nonadiabatic polyatomic systems. This shows that the combination of the dynamical and spectral simulations definitely provides more accurate and detailed information on the microscopic mechanisms of photophysical and photochemical processes. Hence the simulation of time-resolved spectroscopic signals provides another important dimension to examine the accuracy of quantum chemistry methods.

Reduced-dimensional surface hopping with offline-online computations

Molecular dynamics simulations often classically evolve the nuclear geometry on adiabatic potential energy surfaces (PESs), punctuated by random hops between energy levels in regions of strong coupling, in an algorithm known as surface hopping. However, the computational expense of integrating the geometry on a full-dimensional PES and computing the required couplings can quickly become prohibitive as the number of atoms increases. In this work, we describe a method for surface hopping that uses only important reaction coordinates, performs all expensive evaluations of the true PESs and couplings only once before simulating dynamics (offline), and then queries the stored values during the surface hopping simulation (online). Our Python codes are freely available on GitHub. Using photodissociation of azomethane as a test case, this method is able to reproduce experimental results that have thus far eluded ab initio surface hopping studies.

Efficient Approximation of Potential Energy Surfaces with Mixed-Basis Interpolation

The potential energy surface (PES) describes the energy of a chemical system as a function of its geometry and is a fundamental concept in modern chemistry. A PES provides much useful information about the system, including the structures and energies of various stationary points, such as stable conformers (local minima) and transition states (first-order saddle points) connected by a minimum-energy path. Our group has previously produced surrogate reduced-dimensional PESs using sparse interpolation along chemically significant reaction coordinates, such as bond lengths, bond angles, and torsion angles. These surrogates used a single interpolation basis, either polynomials or trigonometric functions, in every dimension. However, relevant molecular dynamics (MD) simulations often involve some combination of both periodic and nonperiodic coordinates. Using a trigonometric basis on nonperiodic coordinates, such as bond lengths, leads to inaccuracies near the domain boundary. Conversely, polynomial interpolation on the periodic coordinates does not enforce the periodicity of the surrogate PES gradient, leading to nonconservation of total energy even in a microcanonical ensemble. In this work, we present an interpolation method that uses trigonometric interpolation on the periodic reaction coordinates and polynomial interpolation on the nonperiodic coordinates. We apply this method to MD simulations of possible isomerization pathways of azomethane between cis and trans conformers. This method is the only known interpolative method that appropriately conserves total energy in systems with both periodic and nonperiodic reaction coordinates. In addition, compared to all-polynomial interpolation, the mixed basis requires fewer electronic structure calculations to obtain a given level of accuracy, is an order of magnitude faster, and is freely available on GitHub.

On-the-Fly Symmetrical Quasi-Classical Dynamics with Meyer-Miller Mapping Hamiltonian for the Treatment of Nonadiabatic Dynamics at Conical Intersections

The on-the-fly version of the symmetrical quasi-classical dynamics method based on the Meyer-Miller mapping Hamiltonian (SQC/MM) is implemented to study the nonadiabatic dynamics at conical intersections of polyatomic systems. The current on-the-fly implementation of the SQC/MM method is based on the adiabatic representation and the dressed momentum. To include the zero-point energy (ZPE) correction of the electronic mapping variables, we employ both the γ-adjusted and γ-fixed approaches. Nonadiabatic dynamics of the methaniminium cation (CH₂NH₂⁺) and azomethane are simulated using the on-the-fly SQC/MM method. For CH₂NH₂⁺, both ZPE correction approaches give reasonable and consistent results. However, for azomethane, the γ-adjusted version of the SQC/MM dynamics behaves much better than the γ-fixed version. Further analysis indicates that it is always recommended to use the γ-adjusted SQC/MM dynamics in the on-the-fly simulation of photoinduced dynamics of polyatomic systems, particularly when the excited state is well separated from the ground state in the Franck-Condon region. This work indicates that the on-the-fly SQC/MM method is a powerful simulation protocol to deal with the nonadiabatic dynamics of realistic polyatomic systems.

Stability and Dissociation of Ethylenedione (OCCO)

This work examines the electronic structure and apparent instability of ethylenedione (OCCO), including an analysis of the singlet and triplet potential energy surfaces along the bending vibrations. While the singlet state is inherently unstable due to the Renner-Teller effect, theory predicts the triplet state to have a stable minimum on the potential energy surface. The stability of the triplet state is examined in detail, taking into account spin-orbit interactions. Using multireference quantum chemical methods, the lifetime of the triplet state is estimated to be in the picosecond range, significantly lower than previously computed. A quasi-atomic molecular orbital (QUAO) analysis is also used to elucidate the nature of bonding along the potential energy surface in both the singlet and triplet states. These calculations confirm the transient nature of the OCCO molecule, although they do not fully explain the lack of experimental detection via spectroscopy, which is known have the capability to probe even shorter lifetimes.

Combined Electron-Diffraction, Spectroscopic, and Theoretical Determination of the Structure of N-Deuterio- trans-Methyldiazene, CH3N═ND. Conformational Effects of the N═N Double Bond

Gas phase electron-diffraction (GED) data obtained at a nozzle-tip temperature of 273 K have been combined with spectroscopic vibrational-rotational constants to determine the structure of trans-methyldiazene, an important prototype for the N═N double bond. The N-deuterio form CH₃N═ND was used in the study since it is appreciably more stable than CH₃N═NH. Both the theoretical and experimental results are consistent with a planar C _s trans-CNND framework. The experimental results ( r_α⁰/ r_g²⁷³) are 1.465(2)/1.467(2) Å for the CN bond, 1.248(1)/1.251(1) Å for the N═N double bond, and 1.037(17)/1.048(17) Å for the ND bond. The NND angle is 105.9(20)/105.6(20)° and the CNN angle is 112.4(5)/112.2(5)°, where the uncertainties in parentheses are twice the standard deviation from a simultaneous least-squares fit of the GED and microwave data. For the methyl group, both theory and experiment indicate that two CH bonds are symmetrically arranged out of the molecular plane while the third CH' lies in the plane in an eclipsed (not staggered) cis-H'CNN arrangement. Theoretical calculations (B3LYP/cc-PVnZ and CCSD(T)/cc-PVnZ) suggest a slight distortion of the methyl group, with a tilt of the methyl top axis about 5° away from the N═N bond. The experimental data are consistent with this picture but are equally consistent with an undistorted methyl group. Inclusion of distortions predicted by theory in a complete basis set limit (CBS) lead to a preferred analysis with average values of 1.086(5)/1.106(5) Å for the CH bond length and an average HCH angle of 108.3(8)/107.8(8)°. Features of the structure of methyldiazene and related compounds are discussed. It is found that the short N═N bond length in the diazenes produces much greater steric repulsion than in analogous ethylene compounds and this effect leads to some interesting conformational and distortion differences for attached CH₃ groups.

Toward a comprehensive definition of oxidation state (IUPAC Technical Report)

A generic definition of oxidation state (OS) is formulated: “The OS of a bonded atom equals its charge after ionic approximation”. In the ionic approximation, the atom that contributes more to the bonding molecular orbital (MO) becomes negative. This sign can also be estimated by comparing Allen electronegativities of the two bonded atoms, but this simplification carries an exception when the more electronegative atom is bonded as a Lewis acid. Two principal algorithms are outlined for OS determination of an atom in a compound; one based on composition, the other on topology. Both provide the same generic OS because both the ionic approximation and structural formula obey rules of stable electron configurations. A sufficiently simple empirical formula yields OS via the algorithm of direct ionic approximation (DIA) by these rules. The topological algorithm works on a Lewis formula (for a molecule) or a bond graph (for an extended solid) and has two variants. One assigns bonding electrons to more electronegative bond partners, the other sums an atom’s formal charge with bond orders (or bond valences) of sign defined by the ionic approximation of each particular bond at the atom. A glossary of terms and auxiliary rules needed for determination of OS are provided, illustrated with examples, and the origins of ambiguous OS values are pointed out. An electrochemical OS is suggested with a nominal value equal to the average OS for atoms of the same element in a moiety that is charged or otherwise electrochemically relevant.

Photophysics and photochemistry of an asymmetrically substituted diazene: a suitable cage effect probe

The photophysics and photochemistry of (1-biphenyl-4-yl-1-methyl-ethyl)-tert-butyl diazene were thoroughly studied by laser flash photolysis from the picosecond to the microsecond time domain. The compound has favorable features as a radical photoinitiator and as a probe for cage effect studies in liquids, supercritical fluids, and compressed gases. The biphenyl moiety acts as an antenna efficiently transferring electronic energy to the dissociative (1)n,pi* state centered on the azo moiety. By picosecond experiments irradiating at the biphenyl- and at the azo-centered transitions, we were able to demonstrate this fact as well as determine a lifetime of 0.7 ps for the buildup of 1-biphenyl-4-yl-1-methyl-ethyl radicals (BME*). The sum of in-cage reaction rate constants of BME* radicals by combination and disproportionation is 5 x 10(10) s(-1). The free radical quantum yield in solution is 0.21 (phi(BME*)) in n-hexane at room temperature, whereas the dissociation quantum yield approaches 50%. The symmetric ketone, 2,4-bis-biphenyl-4-yl-2,4-dimethyl-pentan-2-one, was used as a reference compound for the production and reaction of BME* radicals. Transient IR measurements show CO stretching bands of the excited (3)pi,pi* and (1)n,pi* states but no dissociation up to 0.5 ns. A fluorescence lifetime of 1 ns for this ketone is consistent with this observation. By transient actinometry and kinetic decays in the microsecond time range, we measured epsilon(BME*) = (2.3 +/- 0.2) x 10(4) M(-1) cm(-1) at 325 nm and a second-order rate constant of 5.8 x 10(9) M(-1) s(-1) for the consumption of BME* radicals.

Photolysis of an asymmetrically substituted diazene in solution and in the crystalline state

In this work we study the product distribution in the steady state photolysis of a diazene, (1-biphenyl-4-yl-1-methyl-ethyl)-tert-butyl diazene, and a ketone, 2,4-bis(biphenyl-4-yl)-2,4-dimethyl-pentan-3-one, in the solid state and in solution. The two compounds yield 1-biphenyl-4-yl-1-methyl-ethyl (BME ) radicals upon photolysis. The ketone yields two units of this radical, whereas the diazene yields one BME and one tert-butyl radical. Product analysis of the two compounds in solution makes it possible to differentiate their origin from their corresponding geminate cages, and from the different encounter pairs in the case of the asymmetrically substituted diazene photolysis. In this way we obtain a complete reaction scenery for the diazene, a compound with interesting features as a radical photoinitiator and as a cage effect probe in fluid media. The reaction in cages containing two BME radicals shows a decrease by a factor of 4 in the ratio of combination to disproportionation products upon going from the solid to the liquid phase. On the contrary, the reaction in cages containing a BME and a tert-butyl radical shows a 30-fold increase in combination to disproportionation ratio in liquid compared to the crystal. We analyze the reasons for these differences considering the differences in the reactivity of the radicals and in cage rigidity.