Ab initio/interpolated quantum dynamics on coupled electronic states with full configuration interaction wave functions

Theoretical studies on triplet-state driven dissociation of formaldehyde by quasi-classical molecular dynamics simulation on machine-learning potential energy surface

The H-atom dissociation of formaldehyde on the lowest triplet state (T1) is studied by quasi-classical molecular dynamic simulations on the high-dimensional machine-learning potential energy surface (PES) model. An atomic-energy based deep-learning neural network (NN) is used to represent the PES function, and the weighted atom-centered symmetry functions are employed as inputs of the NN model to satisfy the translational, rotational, and permutational symmetries, and to capture the geometry features of each atom and its individual chemical environment. Several standard technical tricks are used in the construction of NN-PES, which includes the application of clustering algorithm in the formation of the training dataset, the examination of the reliability of the NN-PES model by different fitted NN models, and the detection of the out-of-confidence region by the confidence interval of the training dataset. The accuracy of the full-dimensional NN-PES model is examined by two benchmark calculations with respect to ab initio data. Both the NN and electronic-structure calculations give a similar H-atom dissociation reaction pathway on the T1 state in the intrinsic reaction coordinate analysis. The small-scaled trial dynamics simulations based on NN-PES and ab initio PES give highly consistent results. After confirming the accuracy of the NN-PES, a large number of trajectories are calculated in the quasi-classical dynamics, which allows us to get a better understanding of the T1-driven H-atom dissociation dynamics efficiently. Particularly, the dynamics simulations from different initial conditions can be easily simulated with a rather low computational cost. The influence of the mode-specific vibrational excitations on the H-atom dissociation dynamics driven by the T1 state is explored. The results show that the vibrational excitations on symmetric C-H stretching, asymmetric C-H stretching, and C=O stretching motions always enhance the H-atom dissociation probability obviously.

Machine Learning for Electronically Excited States of Molecules

Electronically excited states of molecules are at the heart of photochemistry, photophysics, as well as photobiology and also play a role in material science. Their theoretical description requires highly accurate quantum chemical calculations, which are computationally expensive. In this review, we focus on not only how machine learning is employed to speed up such excited-state simulations but also how this branch of artificial intelligence can be used to advance this exciting research field in all its aspects. Discussed applications of machine learning for excited states include excited-state dynamics simulations, static calculations of absorption spectra, as well as many others. In order to put these studies into context, we discuss the promises and pitfalls of the involved machine learning techniques. Since the latter are mostly based on quantum chemistry calculations, we also provide a short introduction into excited-state electronic structure methods and approaches for nonadiabatic dynamics simulations and describe tricks and problems when using them in machine learning for excited states of molecules.

Machine Learning for Electronically Excited States of Molecules

Electronically excited states of molecules are at the heart of photochemistry, photophysics, as well as photobiology and also play a role in material science. Their theoretical description requires highly accurate quantum chemical calculations, which are computationally expensive. In this review, we focus on not only how machine learning is employed to speed up such excited-state simulations but also how this branch of artificial intelligence can be used to advance this exciting research field in all its aspects. Discussed applications of machine learning for excited states include excited-state dynamics simulations, static calculations of absorption spectra, as well as many others. In order to put these studies into context, we discuss the promises and pitfalls of the involved machine learning techniques. Since the latter are mostly based on quantum chemistry calculations, we also provide a short introduction into excited-state electronic structure methods and approaches for nonadiabatic dynamics simulations and describe tricks and problems when using them in machine learning for excited states of molecules.

Molecular excited states through a machine learning lens

Theoretical simulations of electronic excitations and associated processes in molecules are indispensable for fundamental research and technological innovations. However, such simulations are notoriously challenging to perform with quantum mechanical methods. Advances in machine learning open many new avenues for assisting molecular excited-state simulations. In this Review, we track such progress, assess the current state of the art and highlight the critical issues to solve in the future. We overview a broad range of machine learning applications in excited-state research, which include the prediction of molecular properties, improvements of quantum mechanical methods for the calculations of excited-state properties and the search for new materials. Machine learning approaches can help us understand hidden factors that influence photo-processes, leading to a better control of such processes and new rules for the design of materials for optoelectronic applications.

Constructing an Interpolated Potential Energy Surface of a Large Molecule: A Case Study with Bacteriochlorophyll a Model in the Fenna-Matthews-Olson Complex

Constructing a reliable potential energy surface (PES) is a key step toward computationally studying the chemical dynamics of any molecular system. The interpolation scheme is a useful tool that can closely follow the accuracy of quantum chemical means at a dramatically reduced computational cost. However, applying interpolation to building a PES of a large molecule is not a straightforward black-box approach, as it frequently encounters practical difficulties associated with its large dimensionality. Here, we present detailed courses of applying interpolation toward building a PES of a large chromophore molecule. We take the example of S₀ and S₁ electronic states of bacteriochlorophyll a (BChla) molecules in the Fenna-Matthews-Olson light harvesting complex. With a reduced model molecule that bears BChla's main π-conjugated ring, various practical approaches are designed for improving the PES quality in a stable manner and for fine-tuning the final surface such that the surface can be adopted for long time molecular dynamics simulations. Combined with parallel implementation, we show that interpolated mechanics/molecular mechanics (IM/MM) simulations of the entire complex in the nanosecond time scale can be conducted readily without any practical issues. With 1500 interpolation data points for each chromophore unit, the PES error relative to the reference quantum chemical calculation is found to be ∼0.15 eV in the thermally accessible region of the conformational space, together with ∼0.01 eV error in S₀ - S₁ transition energies. The performance issue related to the use of a large interpolation database within the framework of our parallel routines is also discussed.

Investigation of spin-flip reactions of Zr + CH3CN by relativistic density functional theory

To explore the details of the reaction mechanisms of Zr atoms with acetonitrile molecules, the triplet and singlet spin-state potential energy surfaces have been investigated. Density functional theory (DFT) with the relativistic zero-order regular approximation at the PW91/TZ2P level has been applied. The complicated minimum energy reaction path involves four transition states (TS), stationary states 1-5 and one spin inversion (indicated by ⇒): (3)Zr + NCCH(3) → (3)Zr-η(1)-NCCH(3) ((3)1) → (3)TS(1/2) → (3)Zr-η(2)-(NC)CH(3) ((3)2) → (3)TS(2/3) → (3)ZrH-η(3)-(NCCH(2)) ((3)3) → (3)TS(3/4) → CNZrCH(3) ((3)4) ⇒ (1)TS(4/5) → CN(ZrH)CH(2) ((1)5). The minimum energy crossing point was determined with the help of the DFT fractional-occupation-number approach. The spin inversion leading from the triplet to the singlet state facilitates the activation of a C-H bond, lowering the rearrangement-barrier by 78 kJ/mol. The overall reaction is calculated to be exothermic by about 296 kJ/mol. All intermediate and product species were frequency and NBO analyzed. The species can be rationalized with the help of Lewis type formulas.

FIRST PRINCIPLES MOLECULAR DYNAMICS INVOLVING EXCITED STATES AND NONADIABATIC TRANSITIONS

Extensions of traditional molecular dynamics to excited electronic states and non-Born–Oppenheimer dynamics are reviewed focusing on applicability to chemical reactions of large molecules, possibly in condensed phases. The latter imposes restrictions on both the level of accuracy of the underlying electronic structure theory and the treatment of nonadiabaticity. This review, therefore, exclusively deals with ab initio "on the fly" molecular dynamics methods. For the same reason, mainly mixed quantum-classical approaches to nonadiabatic dynamics are considered.

CONSTRUCTION OF A GLOBAL POTENTIAL ENERGY SURFACE FROM NOVEL AB INITIO MOLECULAR DYNAMICS FOR THE O(3P) + C3H3 REACTION

We present a global potential energy surface (PES) for the 2 A state of the O (3 P ) + C 3 H 3 radical reaction. The global PES is constructed mainly using direct ab initio molecular dynamics and further sampling is done using the Diffusion Monte Carlo method. The potential is fully invariant with respect to permutational symmetry of like atoms. Special techniques, based on invariant theory of finite groups, have been used to develop basis functions for fitting that display this symmetry. The resultant potential energy surface shows multiple reaction paths with six different product channels. The products of the reactions are CO + C 2 H 3 radicals H + C 3 H 2 O radicals (with two isomers, propynal and propa-1,2-dien-1-one) and OH + C 3 H 2 radicals (with three isomers, vinylidenecarbene, propargylene and cyclopropenylidene). Energies of the PES are in excellent agreement with ab initio energies for each stationary point, the reactants and the products. Most stationary points are fitted at the sub Kcal/mol level. The global potential surface represents all the stationary points and six different product channels correctly. Preliminary dynamics calculations show abstraction and insertion mechanisms for the OH + vinylidenecarbene channel and the H + propynal channel, respectively.

Matching-pursuit/split-operator-Fourier-transform simulations of excited-state nonadiabatic quantum dynamics in pyrazine

A simple approach for numerically exact simulations of nonadiabatic quantum dynamics in multidimensional systems is introduced and applied to the description of the photoabsorption spectroscopy of pyrazine. The propagation scheme generalizes the recently developed matching-pursuit/split-operator-Fourier-transform (MP/SOFT) method [Y. Wu and V. S. Batista, J. Chem. Phys. 121, 1676 (2004)] to simulations of nonadiabatic quantum dynamics. The time-evolution operator is applied, as defined by the Trotter expansion to second order accuracy, in dynamically adaptive coherent-state expansions. These representations are obtained by combining the matching-pursuit algorithm with a gradient-based optimization method. The accuracy and efficiency of the resulting computational approach are demonstrated in calculations of time-dependent survival amplitudes and photoabsorption cross sections, using a model Hamiltonian that allows for direct comparisons with benchmark calculations. Simulations in full-dimensional potential energy surfaces involve the propagation of a 24-dimensional wave packet to describe the S(1)S(2) interconversion of pyrazine after S(0)-->S(2) photoexcitation. The reported results show that the generalized MP/SOFT method is a practical and accurate approach to model nonadiabatic reaction dynamics in polyatomic systems.

Matching-pursuit∕split-operator Fourier-transform simulations of nonadiabatic quantum dynamics

A rigorous and practical approach for simulations of nonadiabatic quantum dynamics is introduced. The algorithm involves a natural extension of the matching-pursuitsplit-operator Fourier-transform (MPSOFT) method [Y. Wu and V. S. Batista, J. Chem. Phys. 121, 1676 (2004)] recently developed for simulations of adiabatic quantum dynamics in multidimensional systems. The MPSOFT propagation scheme, extended to nonadiabatic dynamics, recursively applies the time-evolution operator as defined by the standard perturbation expansion to first-, or second-order, accuracy. The expansion is implemented in dynamically adaptive coherent-state representations, generated by an approach that combines the matching-pursuit algorithm with a gradient-based optimization method. The accuracy and efficiency of the resulting propagation method are demonstrated as applied to the canonical model systems introduced by Tully for testing simulations of dual curve-crossing nonadiabatic dynamics.

Matching-pursuit/split-operator-Fourier-transform computations of thermal correlation functions

A rigorous and practical methodology for evaluating thermal-equilibrium density matrices, finite-temperature time-dependent expectation values, and time-correlation functions is described. The method involves an extension of the matching-pursuit/split-operator-Fourier-transform method to the solution of the Bloch equation via imaginary-time propagation of the density matrix and the evaluation of Heisenberg time-evolution operators through real-time propagation in dynamically adaptive coherent-state representations.

Interpolation of diabatic potential energy surfaces

A method is presented for constructing diabatic potential energy matrices from ab initio quantum chemistry data. The method is similar to that reported previously for single adiabatic potential energy surfaces, but correctly accounts for the nuclear permutation symmetry of diabatic potential energy matrices and other complications that arise from the derivative coupling of electronic states. The method is tested by comparison with an analytic model for the two lowest energy states of H(3).

Long live vinylidene! A new view of the H(2)C=C: --> HC triple bond CH rearrangement from ab initio molecular dynamics

We present complete active space self-consistent field (CASSCF) ab initio molecular dynamics (AIMD) simulations of the preparation of the metastable species vinylidene, and its subsequent, highly exothermic isomerization to acetylene, via electron removal from vinylidene anion (D(2)C=C(-) --> D(2)C=C: --> DC triple bond CD). After equilibrating vinylidene anion-d(2) at either 600 +/- 300 K (slightly below the isomerization barrier) or 1440 K +/- 720 K (just above the isomerization barrier), we remove an electron to form a vibrationally excited singlet vinylidene-d(2) and follow its dynamical evolution for 1.0 ps. Remarkably, we find that none of the vinylidenes equilibrated at 600 K and only 20% of the vinylidenes equilibrated at 1440 K isomerized, suggesting average lifetimes >1 ps for vibrationally excited vinylidene-d(2). Since the anion and neutral vinylidene are structurally similar, and yet extremely different geometrically from the isomerization transition state (TS), neutral vinylidene is not formed near the TS so that it must live until it has sufficient instantaneous kinetic energy in the correct vibrational mode(s). The origin of the delay is explained via both orbital rearrangement and intramolecular vibrational energy redistribution (IVR) effects. Unique signatures of the isomerization dynamics are revealed in the anharmonic vibrational frequencies extracted from the AIMD, which should be observable by ultrafast vibrational spectroscopy and in fact are consistent with currently available experimental spectra. Most interestingly, of those trajectories that did isomerize, every one of them violated conventional transition-state theory by recrossing back to vinylidene multiple times, against conventional notions that expect highly exothermic reactions to be irreversible. The dynamical motion responsible for the multiple barrier recrossings involves strong mode-coupling between the vinylidene CD(2) rock and a local acetylene DCC bend mode that has been recently observed experimentally. The multiple barrier recrossings can be used, via a generalized definition of lifetime, to reconcile extremely disparate experimental estimates of vinylidene's lifetime (differing by at least 6 orders of magnitude). Last, a caveat: These results are constrained by the approximations inherent in the simulation (classical nuclear motion, neglect of rotation-vibration coupling, and restriction to C(s) symmetry); refinement of these predictions may be necessary when more exact simulations someday become feasible.