First principles determination of the NH2/ND2(Ã,X̃) branching ratios for photodissociation of NH3/ND3 via full-dimensional quantum dynamics based on a new quasi-diabatic representation of coupled ab initio potential energy surfaces

Making Peace with Random Phases: Ab Initio Conical Intersection Quantum Dynamics in Random Gauges

Ab initio modeling of conical intersection wave packet dynamics is crucial for various photochemical, photophysical, and biological processes. However, adiabatic electronic states obtained from electronic structure computations involve random phases, or more generally, random gauge fixings, which cannot be directly used in the modeling of nonadiabatic wave packet simulations. Here we develop a random-gauge local diabatic representation that allows an exact modeling of conical intersection dynamics directly using the adiabatic electronic states with phases randomly assigned during the electronic structure computations. Its utility is demonstrated by an exact ab initio modeling of the two-dimensional Shin-Metiu model with and without an external magnetic field. Our results provide a simple approach to integrating the electronic structure computations into nonadiabatic quantum dynamics, thus paving the way for ab initio modeling of conical intersection dynamics.

Generalized Semiclassical Ehrenfest Method: A Route to Wave Function-Free Photochemistry and Nonadiabatic Dynamics with Only Potential Energies and Gradients

We reconsider recent methods by which direct dynamics calculations of electronically nonadiabatic processes can be carried out while requiring only adiabatic potential energies and their gradients. We show that these methods can be understood in terms of a new generalization of the well-known semiclassical Ehrenfest method. This is convenient because it eliminates the need to evaluate electronic wave functions and their matrix elements along the mixed quantum-classical trajectories. The new approximations and procedures enabling this advance are the curvature-driven approximation to the time-derivative coupling, the generalized semiclassical Ehrenfest method, and a new gradient correction scheme called the time-derivative matrix (TDM) scheme. When spin-orbit coupling is present, one can carry out dynamics calculations in the fully adiabatic basis using potential energies and gradients calculated without spin-orbit coupling plus the spin-orbit coupling matrix elements. Even when spin-orbit coupling is neglected, the method is useful because it allows calculations by electronic structure methods for which nonadiabatic coupling vectors are unavailable. In order to place the new considerations in context, the article starts out with a review of background material on trajectory surface hopping, the semiclassical Ehrenfest scheme, and methods for incorporating decoherence. We consider both internal conversion and intersystem crossing. We also review several examples from our group of successful applications of the curvature-driven approximation.

N-H and N-C Bond Dissociation Pathways in Ultraviolet Photodissociation of Dimethylamine

We investigated the interlinked N-H and N-C photochemistry of primary and secondary amines via the state-resolved detection of vibrationally excited CH3 product and H atom product by 200-235 nm dimethylamine photodissociation using resonance-enhanced multiphoton ionization (REMPI) and velocity map imaging (VMI) techniques. The out-of-plane bending (ν2) vibrationally excited CH3 showed a bimodal translational energy distribution that became unimodal with a near-zero product yield at longer photolysis wavelengths (λphotolysis). In contrast, a unimodal distribution was observed for the C-H stretching (νCH) vibrationally excited CH3 products with an almost constant product yield in the examined λphotolysis region. We ascribed the state-specific energy releases of the CH3 products to two reaction pathways based on calculations of the potential energy surface (PES): the direct N-CH3 dissociation pathway and the indirect N-CH3 dissociation pathway via the N-H bond conical intersection. Meanwhile, the H atom product showed a bimodal energy distribution similar to the ammonia photodissociation model, with an excited-state counterproduct channel that became accessible at a shorter λphotolysis. These results suggest that the N-H and N-C bond dissociations are connected, and these dissociations cause different photochemistry between primary/secondary amines and tertiary amines.

Femtosecond Electronic and Hydrogen Structural Dynamics in Ammonia Imaged with Ultrafast Electron Diffraction

Directly imaging structural dynamics involving hydrogen atoms by ultrafast diffraction methods is complicated by their low scattering cross sections. Here we demonstrate that megaelectronvolt ultrafast electron diffraction is sufficiently sensitive to follow hydrogen dynamics in isolated molecules. In a study of the photodissociation of gas phase ammonia, we simultaneously observe signatures of the nuclear and corresponding electronic structure changes resulting from the dissociation dynamics in the time-dependent diffraction. Both assignments are confirmed by ab initio simulations of the photochemical dynamics and the resulting diffraction observable. While the temporal resolution of the experiment is insufficient to resolve the dissociation in time, our results represent an important step towards the observation of proton dynamics in real space and time.

Representation of Diabatic Potential Energy Matrices for Multiconfiguration Time-Dependent Hartree Treatments of High-Dimensional Nonadiabatic Photodissociation Dynamics

Conventional quantum mechanical characterization of photodissociation dynamics is restricted by steep scaling laws with respect to the dimensionality of the system. In this work, we examine the applicability of the multi-configurational time-dependent Hartree (MCTDH) method in treating nonadiabatic photodissociation dynamics in two prototypical systems, taking advantage of its favorable scaling laws. To conform to the sum-of-product form, elements of the ab initio diabatic potential energy matrix (DPEM) are re-expressed using the recently proposed Monte Carlo canonical polyadic decomposition method, with enforcement of proper symmetry. The MCTDH absorption spectra and product branching ratios are shown to compare well with those calculated using conventional grid-based methods, demonstrating its promise for treating high-dimensional nonadiabatic photodissociation problems.

Internal conversion and intersystem crossing dynamics based on coupled potential energy surfaces with full geometry-dependent spin-orbit and derivative couplings. Nonadiabatic photodissociation dynamics of NH3(A) leading to the NH(X3Σ-, a1Δ) + H2 channel

We simulate the photodissociation of NH₃ originating from its first excited singlet state S₁ into the NH₂ + H (radical) and NH + H₂ (molecular) channels. The states considered are the ground singlet state S₀, the first excited singlet state S₁ and the lowest-lying triplet state T₁, which permit for the first time a uniform treatment of the internal conversion and intersystem crossing. The simulations are based on a diabatic potential energy matrix (DPEM) of S₀, S₁ coupled by a conical intersection seam, as well as a potential energy surface (PES) for T₁ coupled by spin-orbit coupling (SOC) to the two singlet states. The DPEM and PES are fitted to ab initio electronic structure data (ESD) including energies, energy gradients, and derivative couplings. The DPEM also defines an adiabatic to diabatic state (AtD) transformation, which is used to transform the singular adiabatic SOC into a smooth function of the nuclear coordinates in the diabatic representation, allowing the diabatic SOC to be fit to an analytical functional form. ESD and SOC data obtained from these surfaces can serve as input for either quantum or semi-classical characterization of the nonadiabatic dynamics. Using the SHARC suite of programs, nonadiabatic simulations based on over 40 000 semi-classical trajectories assess the convergence of our results. The production of NH + H₂ is not direct, but is only achieved through a quasi-statistical dissociation mechanism after internal conversion to the ground electronic state. This leads to a much lower yield comparing with the main NH₂ + H channel. The NH(X³Σ^_) radical produced through the intersystem crossing from S₀ to T₁ is rare (∼0.2%) compared to NH(a¹Δ) due to the process being spin forbidden.

High-fidelity first principles nonadiabaticity: diabatization, analytic representation of global diabatic potential energy matrices, and quantum dynamics

Nonadiabatic dynamics, which goes beyond the Born-Oppenheimer approximation, has increasingly been shown to play an important role in chemical processes, particularly those involving electronically excited states. Understanding multistate dynamics requires rigorous quantum characterization of both electronic and nuclear motion. However, such first principles treatments of multi-dimensional systems have so far been rather limited due to the lack of accurate coupled potential energy surfaces and difficulties associated with quantum dynamics. In this Perspective, we review recent advances in developing high-fidelity analytical diabatic potential energy matrices for quantum dynamical investigations of polyatomic uni- and bi-molecular nonadiabatic processes, by machine learning of high-level ab initio data. Special attention is paid to methods of diabatization, high fidelity construction of multi-state coupled potential energy surfaces and property surfaces, as well as quantum mechanical characterization of nonadiabatic nuclear dynamics. To illustrate the tremendous progress made by these new developments, several examples are discussed, in which direct comparison with quantum state resolved measurements led to either confirmation of the observation or sometimes reinterpretation of the experimental data. The insights gained in these prototypical systems greatly advance our understanding of nonadiabatic dynamics in chemical systems.

Enabling complete multichannel nonadiabatic dynamics: A global representation of the two-channel coupled, 1,21A and 13A states of NH3 using neural networks

Global coupled three-state two-channel potential energy and property/interaction (dipole and spin-orbit coupling) surfaces for the dissociation of NH₃(Ã) into NH + H₂ and NH₂ + H are reported. The permutational invariant polynomial-neural network approach is used to simultaneously fit and diabatize the electronic Hamiltonian by fitting the energies, energy gradients, and derivative couplings of the two coupled lowest-lying singlet states as well as fitting the energy and energy gradients of the lowest-lying triplet state. The key issue in fitting property matrix elements in the diabatic basis is that the diabatic surfaces must be smooth, that is, the diabatization must remove spikes in the original adiabatic property surfaces attributable to the switch of electronic wavefunctions at the conical intersection seam. Here, we employ the fit potential energy matrix to transform properties in the adiabatic representation to a quasi-diabatic representation and remove the discontinuity near the conical intersection seam. The property matrix elements can then be fit with smooth neural network functions. The coupled potential energy surfaces along with the dipole and spin-orbit coupling surfaces will enable more accurate and complete treatment of optical transitions, as well as nonadiabatic internal conversion and intersystem crossing.

Reinterpreting the vibrational structure in the electronic spectrum of the propargyl cation (H2C3H+) using an efficient and accurate quantum model

The B̃¹A₁ ← X̃¹A₁ absorption spectra of propargyl cations H₂C₃H⁺ and D₂C₃D⁺ were simulated by an efficient two-dimensional (2D) quantum model, which includes the C-C stretch (v₅) and the C≡C stretch (v₃) vibrational modes. The choice of two modes was based on a scheme that can identify the active modes quantitively by examining the normal coordinate displacements (∆Q) directly based on the ab initio equilibrium geometries and frequencies of the X̃¹A₁ and B̃¹A₁ states of H₂C₃H⁺. The spectrum calculated by the 2D model was found to be very close to those calculated by all the higher three-dimensional (3D) quantum models (including v₅, v₃, and another one in 12 modes of H₂C₃H⁺), which validates the 2D model. The calculated B̃¹A₁ ← X̃¹A₁ absorption spectra of both H₂C₃H⁺ and D₂C₃D⁺ are in fairly good agreement with experimental results.

A fundamental invariant-neural network representation of quasi-diabatic Hamiltonians for the two lowest states of H3

The FI-NN approach is capable of representing highly accurate diabatic PESs with particular and complicated symmetry problems.

Exclusive Neural Network Representation of the Quasi-Diabatic Hamiltonians Including Conical Intersections

We propose a numerically simple and straightforward, yet accurate and efficient neural networks-based fitting strategy to construct coupled potential energy surfaces (PESs) in a quasi-diabatic representation. The fundamental invariants are incorporated to account for the complete nuclear permutation inversion symmetry. Instead of derivative couplings or interstate couplings, a so-called modified derivative coupling term is fitted by neural networks, resulting in accurate description of near degeneracy points, such as the conical intersections. The adiabatic energies, energy gradients, and derivative couplings are well reproduced, and the vanishing of derivative couplings as well as the isotropic topography of adiabatic and diabatic energies in asymptotic regions are automatically satisfied. All of these features of the coupled global PESs are requisite for accurate dynamics simulations. Our approach is expected to be very useful in developing highly accurate coupled PESs in a quasi-diabatic representation in an efficient machine learning-based way.

Accurate Neural Network Representation of the Ab Initio Determined Spin-Orbit Interaction in the Diabatic Representation Including the Effects of Conical Intersections

A method for fitting ab initio determined spin-orbit coupling interactions, in the Breit-Pauli approximation, based on quasidiabatic representations using neural network fits is reported. The algorithm generalizes our recently reported neural network approach for representing the dipole interaction. The S₀, S₁, and T₁ states of formaldehyde are used as an example. First, the two singlet states S₀ and S₁ are diabatized with a modified Boys Localization diabatization method. Second, the spin-orbit coupling between singlet and triplet states is transformed to the diabatic representation. This removes the discontinuities in the adiabatic representation. The diabatized spin-orbit couplings are then fit with smooth neural network functions. The analytic representation of spin-orbit coupling interactions in a diabatic basis by neural networks will make accurate full-dimensional quantum dynamical treatment of both internal conversion and intersystem crossing possible, which will help us to gain better understanding of both processes.

Non-adiabatic Excited-State Molecular Dynamics: Theory and Applications for Modeling Photophysics in Extended Molecular Materials

Optically active molecular materials, such as organic conjugated polymers and biological systems, are characterized by strong coupling between electronic and vibrational degrees of freedom. Typically, simulations must go beyond the Born-Oppenheimer approximation to account for non-adiabatic coupling between excited states. Indeed, non-adiabatic dynamics is commonly associated with exciton dynamics and photophysics involving charge and energy transfer, as well as exciton dissociation and charge recombination. Understanding the photoinduced dynamics in such materials is vital to providing an accurate description of exciton formation, evolution, and decay. This interdisciplinary field has matured significantly over the past decades. Formulation of new theoretical frameworks, development of more efficient and accurate computational algorithms, and evolution of high-performance computer hardware has extended these simulations to very large molecular systems with hundreds of atoms, including numerous studies of organic semiconductors and biomolecules. In this Review, we will describe recent theoretical advances including treatment of electronic decoherence in surface-hopping methods, the role of solvent effects, trivial unavoided crossings, analysis of data based on transition densities, and efficient computational implementations of these numerical methods. We also emphasize newly developed semiclassical approaches, based on the Gaussian approximation, which retain phase and width information to account for significant decoherence and interference effects while maintaining the high efficiency of surface-hopping approaches. The above developments have been employed to successfully describe photophysics in a variety of molecular materials.

Representation of coupled adiabatic potential energy surfaces using neural network based quasi-diabatic Hamiltonians: 1,2 2A′ states of LiFH

A general algorithm for determining diabatic representations from adiabatic energies, energy gradients and derivative couplings using neural networks is introduced.

Two-state diabatic potential energy surfaces of ClH2 based on nonadiabatic couplings with neural networks

A neural network-fitting procedure based on nonadiabatic couplings is proposed to generate two-state diabatic PESs with conical intersections.

Modified Gaussian Wave Packet Method for Calculating Initial State Wave Functions in Photodissociation

A modified Gaussian wave packet relaxation method is proposed to calculate the ground state wave function using an expansion of frozen Gaussian wave packets. This new procedure consists of two steps. In the first step, a multidimensional Gaussian product placed at the ground state equilibrium geometry is propagated in imaginary time. The relaxation optimizes the widths of the one-dimensional Gaussians. In the second step, additional Gaussian wave packets with the same widths are placed near the equilibrium geometry, and the corresponding expansion coefficients are optimized using the same relaxation method. This new algorithm is tested in photodissociation of NOCl and NH₃, and the results show good agreement with the exact results in the energy, wave function, and absorption spectrum. In particular, the highly structured absorption spectrum of NH₃ is reproduced, underscoring the accuracy of both the initial wave packet and the excited state propagation.

Active vs. spectator modes in nonadiabatic photodissociation dynamics of the hydroxymethyl radical via the 22A(3s) Rydberg state

The choice of the active degrees of freedom (DOFs) is a pivotal issue in a reduced-dimensional model of quantum dynamics when a full-dimensional one is not feasible. Here, several five-dimensional (5D) models are used to investigate the nonadiabatic photodissociation dynamics of the hydroxymethyl (CH₂OH) radical, which possesses nine internal DOFs, in its lowest absorption band. A normal-mode based scheme is used to identify the active and spectator modes, and its predictions are confirmed by 5D quantum dynamical calculations. Our results underscore the important role of the CO stretching mode in the photodissociation dynamics of CH₂OH, originating from the photo-induced promotion of an electron from the half-occupied π*_CO antibonding orbital to a carbon Rydberg orbital.

Putting David Craig’s Legacy to Work in Nanotechnology and Biotechnology

David Craig (1919–2015) left us with a lasting legacy concerning basic understanding of chemical spectroscopy and bonding. This is expressed in terms of some of the recent achievements of my own research career, with a focus on integration of Craig’s theories with those of Noel Hush to solve fundamental problems in photosynthesis, molecular electronics (particularly in regard to the molecules synthesized by Maxwell Crossley), and self-assembled monolayer structure and function. Reviewed in particular is the relation of Craig’s legacy to: the 50-year struggle to assign the visible absorption spectrum of arguably the world’s most significant chromophore, chlorophyll; general theories for chemical bonding and structure extending Hush’s adiabatic theory of electron-transfer processes; inelastic electron-tunnelling spectroscopy (IETS); chemical quantum entanglement and the Penrose–Hameroff model for quantum consciousness; synthetic design strategies for NMR quantum computing; Gibbs free-energy measurements and calculations for formation and polymorphism of organic self-assembled monolayers on graphite surfaces from organic solution; and understanding the basic chemical processes involved in the formation of gold surfaces and nanoparticles protected by sulfur-bound ligands, ligands whose form is that of Au0-thiyl rather than its commonly believed AuI-thiolate tautomer.

Accurate nonadiabatic dynamics

This Perspective addresses the use of coupled diabatic potential energy surfaces (PESs) together with rigorous quantum dynamics in full or reduced dimensional coordinate spaces to obtain accurate solutions to problems in nonadiabatic dynamics.

A unified diabatic description for electron transfer reactions, isomerization reactions, proton transfer reactions, and aromaticity

A way is found for describing general chemical reactions using diabatic multi-state and “twin-state” models. (Image adapted with permission from https://www.flickr.com/photos/cybaea/64638988/).