David B. Williams-Young

Direct ab Initio (Meta-)Surface-Hopping Dynamics

Tractable methods for studying the molecular dynamics of chemical processes driven by electronic nonadiabaticity are highly sought after to provide insight into, for example, photochemical reaction mechanisms, molecular collisions, and thermalized electronic band structures. Starting from the time-dependent Schrödinger equation for a many-body system, a direct ab initio trajectory surface-hopping (TSH) method relying on an analytical treatment of nonadiabatic couplings between electronic states is developed in this work. An approach that combines time-dependent perturbation theory and explicit time evolution via TSH to expedite calculation of nonadiabatic transition rates, namely, meta-surface-hopping dynamics, is presented, and an extrapolatory approach using time-dependent perturbation theory for recovering unbiased transition rates is assessed. The meta-surface-hopping method is applied to the problem of estimating nonradiative relaxation rates of a photoexcited iminium ion, CH₂NH₂⁺, and evidence for internal consistency of the combined dynamics/perturbation theory approach is presented.

Effective Inclusion of Mechanical and Electrical Anharmonicity in Excited Electronic States: VPT2-TDDFT Route

We present a reliable and cost-effective procedure for the inclusion of anharmonic effects in excited-state energies and spectroscopic intensities by means of second-order vibrational perturbation theory. This development is made possible thanks to a recent efficient implementation of excited-state analytic Hessians and properties within the time-dependent density functional theory framework. As illustrated in this work, by taking advantage of such algorithmic developments, it is possible to perform calculations of excited-state infrared spectra of medium-large isolated molecular systems, with anharmonicity effects included in both the energy and property surfaces. We also explore the use of this procedure for the inclusion of anharmonic effects in the simulation of vibronic bandshapes of electronic spectra and compare the results with previous, more approximate models.

A Well-Tempered Hybrid Method for Solving Challenging Time-Dependent Density Functional Theory (TDDFT) Systems

The time-dependent Hartree-Fock (TDHF) and time-dependent density functional theory (TDDFT) equations allow one to probe electronic resonances of a system quickly and inexpensively. However, the iterative solution of the eigenvalue problem can be challenging or impossible to converge, using standard methods such as the Davidson algorithm for spectrally dense regions in the interior of the spectrum, as are common in X-ray absorption spectroscopy (XAS). More robust solvers, such as the generalized preconditioned locally harmonic residual (GPLHR) method, can alleviate this problem, but at the expense of higher average computational cost. A hybrid method is proposed which adapts to the problem in order to maximize computational performance while providing the superior convergence of GPLHR. In addition, a modification to the GPLHR algorithm is proposed to adaptively choose the shift parameter to enforce a convergence of states above a predefined energy threshold.

Ab Initio Excited-State Transient Raman Analysis

Time-resolved Raman spectroscopy has proven useful for studying the formation of polarons in conjugated polymers, verifying the presence of reactive intermediates in photochemical reactions, investigating nonradiative transitions in the short lifetime of the photoexcited species, and resolving electron-phonon coupling strengths and exciton dissociation in crystalline materials. In this paper, we present an excited state transient Raman analysis protocol combining ab initio direct molecular dynamics, transient excited state Hessian, and excited state nonresonant Raman activities evaluations. Prototypical molecules are used as test cases, showing the evolution of the transient Raman signatures that follow electronic excitation. This protocol provides a direct route to assigning the vibrations implicated in the (photo)dynamics of several (photoactive) systems, complementary to the transient infrared analysis.

Accurate Assignments of Excited-State Resonance Raman Spectra: A Benchmark Study Combining Experiment and Theory

Femtosecond stimulated Raman scattering (FSRS) probes the structural dynamics of molecules in electronically excited states by following the evolution of the vibrational spectrum. Interpreting the dynamics requires accurate assignments to connect the vibrational bands with specific nuclear motions of an excited molecule. However, the assignment of FSRS signals is often complicated by mode-specific resonance enhancement effects that are difficult to calculate for molecules in electronically excited states. We present benchmark results for a series of eight aryl-substituted thiophene derivatives to show that calculated off-resonance Raman spectra can be used to assign experimental bands on the basis of a comparison of structurally similar compounds and careful consideration of the resonance condition. Importantly, we show that direct comparison with the off-resonant calculations can lead to incorrect assignments of the experimental spectrum if the resonance condition is neglected. These results highlight the importance of resonance enhancement effects in assigning FSRS spectra.

Efficient Implementation of Variation after Projection Generalized Hartree–Fock

Projected Hartree-Fock (PHF) theory can restore important symmetries to broken symmetry wave functions. Variation after projection (VAP) implementations make it possible to deliberately break and then restore a given symmetry by directly minimizing the projected energy expression. This technique can be applied to any symmetry that can be broken from relaxing constraints on single Slater determinant wave functions. For instance, generalized Hartree-Fock (GHF) wave functions are eigenfunctions of neither Ŝz nor S2. By relaxing these constraints, the wave function can explore a larger variational space and can reach lower energies than more constrained HF solutions. We have implemented spin-projected GHF (SGHF), which retains many of the advantages of breaking symmetry while also being a spin eigenfunction, with some notable improvements over previous implementations. Our new algorithm involves the formation of new intermediate matrices not previously discussed in the literature. Discretization of the necessary integration over the rotation group SO(3) is also accomplished much more efficiently using Lebedev grids. A novel scheme to incrementally build rotated Fock matrices is also introduced and compared with more standard approaches.

Model Order Reduction Algorithm for Estimating the Absorption Spectrum

The ab initio description of the spectral interior of the absorption spectrum poses both a theoretical and computational challenge for modern electronic structure theory. Due to the often spectrally dense character of this domain in the quantum propagators eigenspectrum for medium-to-large sized systems, traditional approaches based on the partial diagonalization of the propagator often encounter oscillatory and stagnating convergence. Electronic structure methods which solve the molecular response problem through the solution of spectrally shifted linear systems, such as the complex polarization propagator, offer an alternative approach which is agnostic to the underlying spectral density or domain location. This generality comes at a seemingly high computational cost associated with solving a large linear system for each spectral shift in some discretization of the spectral domain of interest. In this work, we present a novel, adaptive solution to this high computational overhead based on model order reduction techniques via interpolation. Model order reduction reduces the computational complexity of mathematical models and is ubiquitous in the simulation of dynamical systems and control theory. The efficiency and effectiveness of the proposed algorithm in the ab initio prediction of X-ray absorption spectra is demonstrated using a test set of challenging water clusters which are spectrally dense in the neighborhood of the oxygen K-edge. On the basis of a single, user defined tolerance we automatically determine the order of the reduced models and approximate the absorption spectrum up to the given tolerance. We also illustrate that, for the systems studied, the automatically determined model order increases logarithmically with the problem dimension, compared to a linear increase of the number of eigenvalues within the energy window. Furthermore, we observed that the computational cost of the proposed algorithm only scales quadratically with respect to the problem dimension.