Mapping Simulated Two-Dimensional Spectra to Molecular Models Using Machine Learning.

Two-dimensional (2D) spectroscopy encodes molecular properties and dynamics into expansive spectral data sets. Translating these data into meaningful chemical insights is challenging because of the many ways chemical properties can influence the spectra. To address the task of extracting chemical information from 2D spectroscopy, we study the capacity of simple feedforward neural networks (NNs) to map simulated 2D electronic spectra to underlying physical Hamiltonians. We examined hundreds of simulated 2D spectra corresponding to monomers and dimers with varied Franck-Condon active vibrations and monomer-monomer electronic couplings. We find the NNs are able to correctly characterize most Hamiltonian parameters in this study with an accuracy above 90%. Our results demonstrate that NNs can aid in interpreting 2D spectra, leading from spectroscopic features to underlying effective Hamiltonians.

Semiglobal diabatic potential energy matrix for the N-H photodissociation of methylamine.

We constructed an analytic diabatic potential energy matrix (DPEM) that describes the N-H photodissociation of methylamine; the electronic state space includes the ground and first excited singlet states. The input for the fit was calculated by extended multi-state complete active space second-order perturbation theory. The data were diabatized using the dipole-quadrupole diabatization method in which we incorporated a coordinate-dependent weighting scheme for the contribution of the quadrupole moments. To make the resulting potential energy surfaces semiglobal, we extended the anchor points reactive potential method, a multiscale approach that assigns the internal coordinates to categories with different levels of computational treatment. Key aspects of the adiabatic potential energy surfaces obtained by diagonalizing the DPEM agree with the available experimental and theoretical data at energies relevant for photochemical studies.

Conservation of Angular Momentum in Direct Nonadiabatic Dynamics.

Direct nonadiabatic dynamics is used to study processes involving multiple electronic states from small molecules to materials. Compared with dynamics with fitted analytical potential energy surfaces, direct dynamics is more user-friendly in that it obtains all needed energies, gradients, and nonadiabatic couplings (NACs) by electronic structure calculations. However, the NAC that is usually used does not conserve angular momentum or the center of mass in widely used mixed quantum-classical nonadiabatic dynamics algorithms, in particular, trajectory surface hopping, semiclassical Ehrenfest, and coherent switching with decay of mixing. We show that by using a projection operator to remove the translational and rotational components of the originally computed NAC, one can restore the conservation.

Extended Hamiltonian molecular dynamics: semiclassical trajectories with improved maintenance of zero point energy.

It is well known that classical trajectories, even if they are initiated with zero point energy (ZPE) in each mode (trajectories initiated this way are commonly called quasiclassical trajectories), do not maintain ZPE in the final states. The energy of high-frequency modes will typically leak into low-frequency modes or relative translation of subsystems during the time evolution. This can lead to severe problems such as unphysical dissociation of a molecule, production of energetically disallowed reaction products, and unphysical product energy distributions. Here a new molecular dynamics method called extended Hamiltonian molecular dynamics (EHMD) is developed to improve the ZPE problem in classical molecular dynamics. In EHMD, two images of a trajectory are connected by one or more springs. The EHMD method is tested with the Henon-Heiles Hamiltonian in reduced and real units and with a Hamiltonian with quartic anharmonicity in real units, and the method is found to improve zero-point maintenance as intended.

Direct diabatization based on nonadiabatic couplings: the N/D method.

Diabatization converts adiabatic electronic states to diabatic states, which can be fit with smooth functions, thereby decreasing the computational time for simulations. Here we present a new diabatization scheme based on components of the nonadiabatic couplings and the adiabatic energy gradients. The nonadiabatic couplings are multi-dimensional vectors that are singular along conical intersection seams, and this makes them essentially impossible to fit; furthermore they have unphysical aspects due to the assumptions of the generalized Born-Oppenheimer scheme, and therefore they are not usually used in diabatization schemes. However, we show here that the nonadiabatic couplings can provide a route to obtaining diabatic states by using the sign change of the energy gradient differences of adiabatic states on paths through conical intersections or locally avoided crossings. We present examples applying the method successfully to several test systems. We compare the method to other diabatization methods previously developed in our group.

Dual-Functional Tamm-Dancoff Approximation with Self-Interaction-Free Orbitals: Vertical Excitation Energies and Potential Energy Surfaces near an Intersection Seam.

Recently we have developed the dual-functional Tamm-Dancoff approximation (DF-TDA) method. DF-TDA is an alternative to linear-response time-dependent density functional theory (LR-TDDFT) with the advantage of providing a correct double-cone topology of S1/S0 conical intersections. In the DF-TDA method, we employ different functionals, which are denoted G and F, for orbital optimization and Hamiltonian construction. We use the notation DF-TDA/G:F. In the current work, we propose that G be the same as F except for having 100% Hartree-Fock exchange. We use the notation F100 to denote functional F with this modification. A motivation for this is that functionals with 100% Hartree-Fock exchange are one-electron self-interaction-free. Here we validate the use of F100/M06 to compute vertical excitation energies and the global potential energy surface of ammonia near a conical intersection to further validate the F100 method for photochemical problems.

Dual-Functional Tamm-Dancoff Approximation: A Convenient Density Functional Method that Correctly Describes S1/S0 Conical Intersections.

Time-dependent Kohn-Sham density functional theory has been used successfully to compute vertical excitation energies, especially for large molecular systems. However, the lack of double excitation character in the excited amplitudes produced by linear response in the adiabatic approximation holds it back from broader applications in photochemistry; for example, it shows (3N - 7)-dimensional conical intersection seams (where N is the number of atoms) between ground and excited states, although the correct dimensionality is 3N - 8. In this letter, we present a new, conceptually simple, easy-to-implement, and easy-to-use way to employ time-dependent Kohn-Sham density functional theory that has global accuracy comparable with the conventional single-functional version and that recovers the double cone topology of the potential energy surfaces at S1/S0 conical intersection seams. The new method is called the dual-functional Tamm-Dancoff approximation (DF-TDA).