Using phase-space Gaussians to compute the vibrational states of OCHCO+

Development of Parallel On-the-Fly Algorithm for Global Exploration of Conical Intersection Seam Space

Conical intersection (CI) seams are configuration spaces of a molecular system where two or more (spin) adiabatic electronic states are degenerate in energy. They play essential roles in photochemistry because nonradiative decays often occur near the minima of the seam, i.e., the minimum energy CIs (MECIs). Thus, it is important to explore the CI seams and discover the MECIs. Although various approaches exist for CI seam exploration, most of them are local in nature, requiring reasonable initial guesses of geometries and nuclear gradients during the search. Global search algorithms, on the other hand, are powerful because they can fully sample the configurational space and locate important MECIs missed by local algorithms. However, global algorithms are often computationally expensive for large systems due to their poor scalability with respect to the number of degrees of freedom. To overcome this challenge, we develop the parallel on-the-fly Crystal algorithm to globally explore the CI seam space, taking advantage of its superior scaling behavior. Specifically, Crystal is coupled with on-the-fly evaluations of the excited and ground state energies using multireference electronic structure methods. Meanwhile, the algorithm is parallelized to further boost its computational efficiency. The effectiveness of this new algorithm is tested for three types of molecular photoswitches of significant importance in material and biomedical sciences: photostatin (PST), stilbene, and butadiene. A rudimentary implementation of the algorithm is applied to PST and stilbene, resulting in the discovery of all previously identified MECIs and several new ones. A refined version of the algorithm, combined with a systematic clustering technique, is applied to butadiene, resulting in the identification of an unprecedented number of energetically accessible MECIs. The results demonstrate that the parallel on-the-fly Crystal algorithm is a powerful tool for automated global CI seam exploration.

"On-the-fly" Crystal : How to reliably and automatically characterize and construct potential energy surfaces

In this work, the Crystal  code, developed previously by the authors to find "holes" as well as legitimate transition states in existing potential energy surface (PES) functions [JPC Lett. 11, 6468 (2020)], is retooled to perform on-the-fly "direct dynamics"-type PES explorations, as well as automatic construction of new PES functions. In all of these contexts, the chief advantage of Crystal  over other methods is its ability to globally map the PES, thereby determining the most relevant regions of configuration space quickly and reliably-even when the dimensionality is rather large. Here, Crystal  is used to generate a uniformly spaced grid of density functional theory (DFT) or ab initio points, truncated over the relevant regions, which can then be used to either: (a) hone in precisely on PES features such as minima and transition states, or; (b) create a new PES function automatically, via interpolation. Proof of concept is demonstrated via application to three molecular systems: water (H2 O), (reduced-dimensional) methane (CH4 ), and methylene imine (CH2 NH).

Hitting the Trifecta: How to Simultaneously Push the Limits of Schrödinger Solution with Respect to System Size, Convergence Accuracy, and Number of Computed States

Methods for solving the Schrödinger equation without approximation are in high demand but are notoriously computationally expensive. In practical terms, there are just three primary factors that currently limit what can be achieved: 1) system size/dimensionality; 2) energy level excitation; and 3) numerical convergence accuracy. Broadly speaking, current methods can deliver on any two of these three goals, but achieving all three at once remains an enormous challenge. In this paper, we shall demonstrate how to "hit the trifecta" in the context of molecular vibrational spectroscopy calculations. In particular, we compute the lowest 1000 vibrational states for the six-atom acetonitrile molecule (CH₃CN), to a numerical convergence of accuracy 10^-2 cm^-1 or better. These calculations encompass all vibrational states throughout most of the dynamically relevant range (i.e., up to ∼4250 cm^-1 above the ground state), computed in full quantum dimensionality (12 dimensions), to near spectroscopic accuracy. To our knowledge, no such vibrational spectroscopy calculation has ever previously been performed.

Molecular Spectra Calculations Using an Optimized Quasi-Regular Gaussian Basis and the Collocation Method

We revisit the collocation method of Manzhos and Carrington [ J. Chem. Phys., 2016, 145, 224110] in which a distributed localized (e.g., Gaussian) basis is used to set up a generalized eigenvalue problem to compute the eigenenergies and eigenfunctions of a molecular vibrational Hamiltonian. Although the resulting linear algebra problem involves full matrices, the method provides a number of important advantages, namely, (i) it is very simple both conceptually and numerically, (ii) it can be formulated using any set of internal molecular coordinates, (iii) it is flexible with respect to the choice of the basis, (iv) no integrals need to be computed, and (v) it has the potential to significantly reduce the basis size through optimizing the placement and the shapes of the basis functions. In the present paper, we explore the latter aspect of the method using the recently introduced, and here further improved, quasi-regular grids (QRGs). By computing the eigenenergies of the four-atom molecule of formaldehyde, we demonstrate that a QRG-based distributed Gaussian basis is superior to the previously used choices.

Local Measure of Quantum Effects in Quantum Dynamics

The Madelung-de Broglie-Bohm formulation of the Schrödinger equation casts the time-evolution of a wave function as dynamics of an ensemble of quantum, or Bohmian, trajectories, interacting via the nonlocal quantum potential. This trajectory perspective gives insight into the quantumness (or classicality) of a given system due to clear partitioning of the energy into classical and quantum components. Here, we propose a system-independent measure of the quantumness of dynamics, based on the energy time-change, referred to as "quantum power". This measure is local in the coordinate space. Based on applications to model chemical systems, we argue that during the transition from the quantum to classical regime, defined as compression of quantization, the quantum features in dynamics do not "disappear" but are pushed forward in time. This feature may be used to gauge the validity of the semiclassical and other approximate dynamics approaches in applications to anharmonic systems.

Spectroscopy and Scattering Studies Using Interpolated Ab Initio Potentials

The Born-Oppenheimer potential energy surface (PES) has come a long way since its introduction in the 1920s, both conceptually and in predictive power for practical applications. Nevertheless, nearly 100 years later-despite astonishing advances in computational power-the state-of-the-art first-principles prediction of observables related to spectroscopy and scattering dynamics is surprisingly limited. For example, the water dimer, (H₂O)₂, with only six nuclei and 20 electrons, still presents a formidable challenge for full-dimensional variational calculations of bound states and is considered out of reach for rigorous scattering calculations. The extremely poor scaling of the most rigorous quantum methods is fundamental; however, recent progress in development of approximate methodologies has opened the door to fairly routine high-quality predictions, unthinkable 20 years ago. In this review, in relation to the workflow of spectroscopy and/or scattering studies, we summarize progress and challenges in the component areas of electronic structure calculations, PES fitting, and quantum dynamical calculations.

Analysis of the Proton Transfer Bands in the Infrared Spectra of Linear N2H+···OC and N2D+···OC Complexes Using Electric Field-Driven Classical Trajectories

In this work, we describe ab initio calculations and assignment of infrared (IR) spectra of hydrogen-bonded ion-molecular complexes that involve a fluxional proton: the linear N₂H⁺···OC and N₂D⁺···OC complexes. Given the challenges of describing fluxional proton dynamics and especially its IR activity, we use electric field-driven classical trajectories, i.e., the driven molecular dynamics (DMD) method that was developed by us in recent years and for similar applications, in conjunction with high-level electronic structure theory. Namely, we present a modified and a numerically efficient implementation of DMD specifically for direct (or "on the fly") calculations, which we carry out at the MP2-F12/AVDZ level of theory for the potential energy surface (PES) and MP2/AVDZ for the dipole moment surfaces (DMSs). Detailed analysis of the PES, DMS, and the time-dependence of the first derivative of the DMS, referred to as the driving force, for the highly fluxional vibrations involving H⁺/D⁺ revealed that the strongly non-harmonic PES and non-linear DMS yield remarkably complex vibrational spectra. Interestingly, the classical trajectories reveal a doublet in the proton transfer part of the spectrum with the two peaks at 1800 and 1980 cm^-1. We find that their shared intensity is due to a Fermi-like resonance interaction, within the classical limit, of the H⁺ parallel stretch fundamental and an H⁺ perpendicular bending overtone. This doublet is also observed in the deuterated species at 1360 and 1460 cm^-1.

Plumbing Potentials for Molecules with Up To Tens of Atoms: How to Find Saddle Points and Fix Leaky Holes

Potential energy surfaces (PESs) play an indispensable role in molecular dynamics but are notoriously difficult to flesh out properly in large-dimensional spaces. In particular, the undetected presence of PES holes, i.e., unphysical saddle points beyond which the potential energy drops arbitrarily, can have devastating effects on both classical and quantum dynamics calculations. In this study, the Crystal algorithm is developed as a tool for efficiently and accurately finding PES holes, as well as legitimate saddle points, even in very large-dimensional configuration spaces. The approach is applied to three large-dimensional PESs for molecular systems of current interest: uracil, naphthalene, and formic acid dimer. Low-lying PES holes are discovered and located for the first two systems-including naphthalene, for which no holes were previously suspected, to the best of our knowledge. Likewise, the double-well, double-proton-transfer isomerization saddle point for formic acid dimer is also located.

Double Proton Transfer in the Dimer of Formic Acid: An Efficient Quantum Mechanical Scheme

Double proton transfer plays an important role in biology and chemistry, such as with DNA base pairs, proteins and molecular clusters, and direct information about these processes can be obtained from tunneling splittings. Carboxylic acid dimers are prototypes for multiple proton transfer, of which the formic acid dimer is the simplest one. Here, we present efficient quantum dynamics calculations of ground-state and fundamental excitation tunneling splittings in the formic acid dimer and its deuterium isotopologues. These are achieved with a multidimensional scheme developed by us, in which the saddle-point normal coordinates are chosen, the basis functions are customized for the proton transfer process, and the preconditioned inexact spectral transform method is used to solve the resultant eigenvalue problem. Our computational results are in excellent agreement with the most recent experiments (Zhang et al., 2017; Li et al., 2019).